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Journal articles on the topic 'Burgers equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Kumar, Nand Kishor. "A Review on Burgers' Equations and It's Applications." Journal of Institute of Science and Technology 28, no. 2 (2023): 49–52. http://dx.doi.org/10.3126/jist.v28i2.61073.

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This article presents a brief study on the review of the Burgers' equation. It also gives some concepts/ideas and techniques to solve Burgers' equation. Applying Burgers' equation to traffic flow requires concentrated effort for the solution. We develop our insights on how to obtain the Navier-Stokes equation through our inquiry into Burgers' equation. We also demonstrate how the Cole-Hopf transformation for the viscous Burgers' equation is derived. Finally, we use Burger's equation function as a model for the flow of traffic. Additionally, by employing the linear system method, we are able to

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2

ABDUSALAM, H. A. "MULTIPLE SOLITON SOLUTIONS FOR THE NAGUMO EQUATION AND THE MODIFIED GENERAL BURGERS-FISHER EQUATION." International Journal of Computational Methods 03, no. 03 (2006): 371–81. http://dx.doi.org/10.1142/s0219876206000904.

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A generalized tanh-function method is used for constructing exact travelling wave solutions for Nagumo's equation and the modified generalized Burger-Fisher equation. Also new multiple soliton solutions are obtained for both equations. Limit case of the time delay is studied and the results of the general Burgers-Fisher equations are verified.

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3

Nandhini, K., and M. Sumathi. "New and Modified Homotopy Perturbation Methods for Addressing Burger’s Non-linear Equation." Indian Journal Of Science And Technology 17, no. 38 (2024): 4019–29. http://dx.doi.org/10.17485/ijst/v17i38.2029.

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Objectives: The aim of this study is to find a novel solution procedure for solving a fluid dynamical problem, especially to solve two-dimensional coupled Burger’s non-linear equation. Methods: New and Modified homotopy perturbation techniques are used to solve the two-dimensional coupled Burger’s equation. The methods intend to make homotopy perturbation method a more robust and trustworthy tool for fluid dynamics researchers by addressing convergence concerns, improving solution accuracy and allowing it to handle a broader range of problems. Findings: The solution for two-dimensional coupled

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4

Mohamad- Jawad, Anwar. "The Sine-Cosine Function Method for Exact Solutions of Nonlinear Partial Differential Equations." Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ), no. 2 (October 17, 2021): 120–39. http://dx.doi.org/10.55562/jrucs.v32i2.327.

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The Sine-Cosine function algorithm is applied for solving nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of nonlinear partial differential equations such as, The K(n + 1, n + 1) equation, Schrödinger-Hirota equation, Gardner equation, the modified KdV equation, perturbed Burgers equation, general Burger’s-Fisher equation, and Cubic modified Boussinesq equation which are the important Soliton equations.Keywords: Nonlinear PDEs, Exact Solutions, Nonlinear Waves, Gardner equation, Sine-Cosine function method, The Schrödinger-Hirota e

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5

Vaganan, B. Mayil, and T. Jeyalakshmi. "Generalized Burgers Equations Transformable to the Burgers Equation." Studies in Applied Mathematics 127, no. 3 (2011): 211–20. http://dx.doi.org/10.1111/j.1467-9590.2010.00515.x.

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6

Ihsan, Hisyam, Syafruddin Side, and Muhammad Iqbal. "Solusi Persamaan Burgers Inviscid dengan Metode Pemisahan Variabel." Journal of Mathematics Computations and Statistics 4, no. 2 (2021): 88. http://dx.doi.org/10.35580/jmathcos.v4i2.24442.

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Penelitian ini mengkaji tentang solusi persamaan Burgers Inviscid dengan metode pemisahan variabel. Tujuan dari penelitian ini adalah untuk mengetahui penyederhanaan sistem persamaan Navier-Stokes menjadi persamaan Burgers Inviscid, menemukan solusi persamaan Burgers Inviscid dengan metode pemisahan variabel, dan melakukan simulasi solusi persamaan dengan menggunakan software Maple18. Persamaan Burgers muncul sebagai penyederhanaan model yang rumit dari sistem persamaan Navier-Stokes. Persamaan Burgers adalah persamaan diferensial parsial hukum konservasi dan merupakan masalah hiperbolik, yait

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7

Zhang, Lei, Lisha Wang, and Xiaohua Ding. "Exact Finite Difference Scheme and Nonstandard Finite Difference Scheme for Burgers and Burgers-Fisher Equations." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/597926.

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We present finite difference schemes for Burgers equation and Burgers-Fisher equation. A new version of exact finite difference scheme for Burgers equation and Burgers-Fisher equation is proposed using the solitary wave solution. Then nonstandard finite difference schemes are constructed to solve two equations. Numerical experiments are presented to verify the accuracy and efficiency of such NSFD schemes.

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8

K, Nandhini, and Sumathi M. "New and Modified Homotopy Perturbation Methods for Addressing Burger's Non-linear Equation." Indian Journal of Science and Technology 17, no. 38 (2024): 4019–29. https://doi.org/10.17485/IJST/v17i38.2029.

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Abstract <strong>Objectives:</strong> The aim of this study is to find a novel solution procedure for solving a fluid dynamical problem, especially to solve two-dimensional coupled Burger’s non-linear equation. <strong>Methods:</strong> New and Modified homotopy perturbation techniques are used to solve the two-dimensional coupled Burger’s equation. The methods intend to make homotopy perturbation method a more robust and trustworthy tool for fluid dynamics researchers by addressing convergence concerns, improving solution accuracy and allowing it to handle a broader

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9

Mohamad Jawad, Anwar Ja’afar, Marko D. Petković, and Anjan Biswas. "Soliton solutions of Burgers equations and perturbed Burgers equation." Applied Mathematics and Computation 216, no. 11 (2010): 3370–77. http://dx.doi.org/10.1016/j.amc.2010.04.066.

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10

Bukhari, Fahren, Sri Nurdiati, Mochamad Tito Julianto, Mohamad Khoirun Najib, and Ruben Harry Valentdio. "IMPLEMENTASI PENYELESAIAN PERSAMAAN BURGERS DENGAN METODE BEDA HINGGA DALAM BAHASA PEMROGRAMAN JULIA." MILANG Journal of Mathematics and Its Applications 19, no. 1 (2023): 1–9. http://dx.doi.org/10.29244/milang.19.1.1-9.

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Burgers equation is a partial differential equation used to modelling several events related to fluids. Burgers equation was firstly introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948. This study discusses solving Burgers equations with finite difference method. In this study, several parameters have been known for the Burgers equation and several cases of partitions are used in finite difference method. The result shows that the more partitions used, the numerical result obtained will be closer to the exact values. In this study, calculations are numeri

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11

Yan, Zhenya. "Complex PT -symmetric nonlinear Schrödinger equation and Burgers equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (2013): 20120059. http://dx.doi.org/10.1098/rsta.2012.0059.

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The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg–de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schrödinger equations (known as the Gross–Pitaevskii equation in Bose–Einstein condensates) with several complex -symmetric potentials. Finally,

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12

Chen, Mei-Dan, and Biao Li. "Classification and Recursion Operators of Dark Burgers’ Equation." Zeitschrift für Naturforschung A 73, no. 2 (2018): 175–80. http://dx.doi.org/10.1515/zna-2017-0324.

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AbstractWith the help of symbolic computation, two types of complete scalar classification for dark Burgers’ equations are derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark Burgers’ systems; so some special equations including symmetry equation and dual symmetry equation are obtained by selecting the free parameter. Furthermore, two kinds of recursion operators for these dark Burgers’ equations are constructed by two direct assumption methods.

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13

Dag, Idris, Dursun Irk, and Ali Sahin. "B-spline collocation methods for numerical solutions of the Burgers' equation." Mathematical Problems in Engineering 2005, no. 5 (2005): 521–38. http://dx.doi.org/10.1155/mpe.2005.521.

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Both time- and space-splitted Burgers' equations are solved numerically. Cubic B-spline collocation method is applied to the time-splitted Burgers' equation. Quadratic B-spline collocation method is used to get numerical solution of the space-splitted Burgers' equation. The results of both schemes are compared for some test problems.

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14

Parumasur, Nabendra, Rasheed A. Adetona, and Pravin Singh. "Efficient Solution of Burgers’, Modified Burgers’ and KdV–Burgers’ Equations Using B-Spline Approximation Functions." Mathematics 11, no. 8 (2023): 1847. http://dx.doi.org/10.3390/math11081847.

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This paper discusses the application of the orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions on partial differential equations. Collocation is performed at Gaussian points to obtain an optimal solution, hence the name orthogonal collocation. The method is used to solve various cases of Burgers’ equations, including the modified Burgers’ equation. The KdV–Burgers’ equation is considered as a test case for the OCFE method using cubic splines. The results compare favourably with existing results. The stability and convergence of the method

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15

WANG, GANGWEI. "SYMMETRY ANALYSIS, ANALYTICAL SOLUTIONS AND CONSERVATION LAWS OF A GENERALIZED KdV–BURGERS–KURAMOTO EQUATION AND ITS FRACTIONAL VERSION." Fractals 29, no. 04 (2021): 2150101. http://dx.doi.org/10.1142/s0218348x21501012.

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Wave motions play an important role in fluid dynamics and engineering issues. In this paper, a systematic study to the generalized KdV–Burgers–Kuramoto equation is presented resort to symmetry method. First, based on the Lie point symmetries of the generalized KdV–Burgers–Kuramoto equation, we get invariants and invariant solutions. In particular, we obtain series solutions of generalized KdV–Burgers–Kuramoto equation. Meanwhile, we find that this equation just exists in Lie point symmetries. Then, we present a conservation law, and derive reciprocal Bäcklund transformations of conservation la

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16

Akkoyunlu, Canan. "FIFTH-ORDER COMPACT FINITE DIFFERENCE SCHEME FOR BURGERS-HUXLEY EQUATION." İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi 24, no. 47 (2025): 249–60. https://doi.org/10.55071/ticaretfbd.1627642.

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The Burgers-Huxley equation arises in several problems in science. The compact finite difference scheme (CFDS) has been developed for the Burgers-Huxley equation. This scheme has been compared different methods for the Burgers-Huxley equation. Dispersive properties are investigated for the linearized equations to examine the nonlinear dynamics after discretisation. The accuracy and computational efficiency of the compact finite differences scheme are shown in numerical test problems.

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17

Bulut, Hasan, Münevver Tuz, and Tolga Akturk. "New Multiple Solution to the Boussinesq Equation and the Burgers-Like Equation." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/952614.

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By considering an improved tanh function method, we found some exact solutions of Boussinesq and Burgers-like equations. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. We found some exact solutions of the Boussinesq equation and the Burgers-like equation.

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18

Gubinelli, Massimiliano, and Nicolas Perkowski. "The infinitesimal generator of the stochastic Burgers equation." Probability Theory and Related Fields 178, no. 3-4 (2020): 1067–124. http://dx.doi.org/10.1007/s00440-020-00996-5.

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Abstract We develop a martingale approach for a class of singular stochastic PDEs of Burgers type (including fractional and multi-component Burgers equations) by constructing a domain for their infinitesimal generators. It was known that the domain must have trivial intersection with the usual cylinder test functions, and to overcome this difficulty we import some ideas from paracontrolled distributions to an infinite dimensional setting in order to construct a domain of controlled functions. Using the new domain, we are able to prove existence and uniqueness for the Kolmogorov backward equati

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19

Li, Xiangzheng, Jinliang Zhang, and Mingliang Wang. "Decay Mode Solutions to (2 + 1)-Dimensional Burgers Equation, Cylindrical Burgers Equation and Spherical Burgers Equation." Journal of Applied Mathematics and Physics 05, no. 05 (2017): 1009–15. http://dx.doi.org/10.4236/jamp.2017.55088.

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20

Magagula, V. M., S. S. Motsa, and P. Sibanda. "A Multi-Domain Bivariate Pseudospectral Method for Evolution Equations." International Journal of Computational Methods 14, no. 04 (2017): 1750041. http://dx.doi.org/10.1142/s0219876217500414.

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In this paper, we present a new general approach for solving nonlinear evolution partial differential equations. The novelty of the approach is in the combination of spectral collocation and Lagrange interpolation polynomials with Legendre–Gauss–Lobatto grid points to descritize and solve equations in piece-wise defined intervals. The method is used to solve several nonlinear evolution partial differential equations, namely, the modified KdV–Burgers equation, modified KdV equation, Fisher’s equation, Burgers–Fisher equation, Burgers–Huxley equation and the Fitzhugh–Nagumo equation. The results

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21

Ahmad, Khalil, and Khudija Bibi. "New Exact Solutions of Burgers’ Equation Using Power Index Method." Discrete Dynamics in Nature and Society 2022 (April 9, 2022): 1–9. http://dx.doi.org/10.1155/2022/5211625.

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In this article, we focus on the new exact solutions of Burger’s equation by using a new technique which is known as the power index method (PIM). In this method, we choose suitable indexes of independent variables and similarity transformation so that the partial differential equation may be converted into ODE. We have obtained analytic solution of the ODE by using symbolic package Maple. We have got exact solution of Burgers’ equation by using analytic solution of ODE and similarity transformation. The proposed method has been effectively employed to find new exact solutions for the nonlinea

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22

Jitsom, Bubpha, Surattana Sungnul, and Ekkachai Kunnawuttipreechachan. "Exact Solutions of the Modified Nonlinear Burgers' Equation." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 18 (December 21, 2023): 469–77. http://dx.doi.org/10.37394/23203.2023.18.50.

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The expansion approach has been used to solve the modified nonlinear Burgers' equation, which has a nonlinear convection term, a viscosity term, and a time-dependent term in its structure. In this paper, the main focus is to find exact solutions of the modified nonlinear Burgers' equation. The (G′=G)-expansion method is one of the methods used to find exact solutions of nonlinear problems. It requires an appropriate transform equation to convert partial differential equations to ordinary differential equations, making it easier to find the solution. In this work, we choose the traveling wave e

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23

Boules, Adel N. "On the existence of the solution of Burgers' equation forn≤4." International Journal of Mathematics and Mathematical Sciences 13, no. 4 (1990): 645–50. http://dx.doi.org/10.1155/s0161171290000898.

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In this paper a proof of the existence of the solution of Burgers' equation forn≤4is presented. The technique used is shown to be valid for equations with more general types of nonlinearities than is present in Burgers' equation.

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24

XIE, YUANXI. "A COMBINATION METHOD AND ITS APPLICATIONS TO NONLINEAR EVOLUTION EQUATIONS." International Journal of Modern Physics B 26, no. 16 (2012): 1250110. http://dx.doi.org/10.1142/s021797921250110x.

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In this paper, a combination method is developed to construct the explicit and exact solutions of nonlinear evolution equations (NEEs). As illustrative examples, the explicit and exact solutions of some physically significant NEEs, comprising the generalized BBM–Burgers equation, generalized KdV–Burgers equation and generalized Benney equation are successfully presented by this means.

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25

Adomian, G. "Stochastic Burgers' equation." Mathematical and Computer Modelling 22, no. 8 (1995): 103–5. http://dx.doi.org/10.1016/0895-7177(95)00159-y.

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26

Hamanaka, Masashi, and Kouichi Toda. "Noncommutative Burgers equation." Journal of Physics A: Mathematical and General 36, no. 48 (2003): 11981–98. http://dx.doi.org/10.1088/0305-4470/36/48/006.

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27

Da Prato, Guiseppe, Arnaud Debussche, and Roger Temam. "Stochastic Burgers' equation." Nonlinear Differential Equations and Applications NoDEA 1, no. 4 (1994): 389–402. http://dx.doi.org/10.1007/bf01194987.

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28

XIE, YUANXI. "SOLVING THE GENERALIZED BURGERS–KdV EQUATION BY A COMBINATION METHOD." Modern Physics Letters B 22, no. 21 (2008): 2021–25. http://dx.doi.org/10.1142/s0217984908016686.

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In view of the analysis on the characteristics of the generalized Burgers equation, generalized KdV equation and generalized Burgers–KdV equation, a combination method is presented to seek the explicit and exact solutions to the generalized Burgers–KdV equation by combining with those of the generalized Burgers equation and generalized KdV equation. As a result, many explicit and exact solutions for the generalized Burgers–KdV equation are successfully obtained by this technique.

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29

İnan, B., and A. R. Bahadir. "Numerical solutions of the generalized Burgers-Huxley equation by implicit exponential finite difference method." Journal of Applied Mathematics, Statistics and Informatics 11, no. 2 (2015): 57–67. http://dx.doi.org/10.1515/jamsi-2015-0012.

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Abstract In this paper, numerical solutions of the generalized Burgers-Huxley equation are obtained using a new technique of forming improved exponential finite difference method. The technique is called implicit exponential finite difference method for the solution of the equation. Firstly, the implicit exponential finite difference method is applied to the generalized Burgers-Huxley equation. Since the generalized Burgers-Huxley equation is nonlinear the scheme leads to a system of nonlinear equations. Secondly, at each time-step Newton’s method is used to solve this nonlinear system then li

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30

Zhang, Liping, Jiangqiong Zheng, Chenxiao Liu, and Jun Ma. "The shock wave solutions of modified ZK Burgers equation in inhomogeneous dusty plasmas." Zeitschrift für Naturforschung A 77, no. 3 (2021): 249–57. http://dx.doi.org/10.1515/zna-2021-0283.

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Abstract This paper offers a shock wave solution to modified Zakharov–Kuznetsov (MZK) Burgers equation in inhomogeneous dusty plasmas with external magnetic field. For this purpose, the fluid equations are reduced to an MZK Burgers equation containing variable coefficients by reductive perturbation method. With the aid of travelling-wave transformation technique, we obtain the analytical oscillatory shock wave solution and monotonic shock wave solution for MZK Burgers equation. The effects of inhomogeneity, external magnetic field, dust charge variation on characteristics of two types of shock

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31

Motsa, S. S., V. M. Magagula, and P. Sibanda. "A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations." Scientific World Journal 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/581987.

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This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accu

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Li, Lingxiao, Jinliang Zhang, and Mingliang Wang. "The travelling wave solutions of nonlinear evolution equations with both a dissipative term and a positive integer power term." AIMS Mathematics 7, no. 8 (2022): 15029–40. http://dx.doi.org/10.3934/math.2022823.

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<abstract> <p>The formula of solution to a nonlinear ODE with an undetermined coefficient and a positive integer power term of dependent variable have been obtained by the transformation of dependent variable and $(\frac{{G'}}{G})$-expansion method. The travelling wave reduction ODEs (perhaps, after integration and identical deformation) of a class of nonlinear evolution equations with a dissipative term and a positive integer power term of dependent variable that includes GKdV-Burgers equation, GKP-Burgers equation, GZK-Burgers equation, GBoussinesq equation and GKlein-Gordon equa

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Liu, Mingshuo, Huanhe Dong, Yong Fang, and Yong Zhang. "Lie Symmetry Analysis of Burgers Equation and the Euler Equation on a Time Scale." Symmetry 12, no. 1 (2019): 10. http://dx.doi.org/10.3390/sym12010010.

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As a powerful tool that can be used to solve both continuous and discrete equations, the Lie symmetry analysis of dynamical systems on a time scale is investigated. Applying the method to the Burgers equation and Euler equation, we get the symmetry of the equation and single parameter groups on a time scale. Some group invariant solutions in explicit form for the traffic flow model simulated by a Burgers equation and Euler equation with a Coriolis force on a time scale are studied.

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M. Fares, Mohammad, Usama M. Abdelsalam, and Faiza M. Allehiany. "Travelling Wave Solutions for Fisher’s Equation Using the Extended Homogeneous Balance Method." Sultan Qaboos University Journal for Science [SQUJS] 26, no. 1 (2021): 22–30. http://dx.doi.org/10.53539/squjs.vol26iss1pp22-30.

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In this work, the extended homogeneous balance method is used to derive exact solutions of nonlinear evolution equations. With the aid of symbolic computation, many new exact travelling wave solutions have been obtained for Fisher’s equation and Burgers-Fisher equation. Fisher’s equation has been widely used in studying the population for various systems, especially in biology, while Burgers-Fisher equation has many physical applications such as in gas dynamics and fluid mechanics. The method used can be applied to obtain multiple travelling wave solutions for nonlinear partial differential eq

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Xie, Yuan-Xi. "SOLUTIONS TO A CLASS OF NONLINEAR WAVE EQUATIONS." Far East Journal of Applied Mathematics 118, no. 1 (2025): 19–38. https://doi.org/10.17654/0972096025003.

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The Burgers equation, KdV equation and Burgers-KdV equation are real physical modes concerning many branches in physics. In this paper, rich types of explicit and exact travelling wave solutions for these three equations, including the solitary wave solutions, the singular travelling wave solutions, the triangle function periodic wave solutions, etc., are presented by a direct trial function approach. Among them, some are new travelling wave solutions.

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BABAOĞLU, Mine. "Burgers ve coupled Burgers denklemlerinin tam ve nümerik çözümleri üzerine." Ordu Üniversitesi Bilim ve Teknoloji Dergisi 12, no. 1 (2022): 1–10. http://dx.doi.org/10.54370/ordubtd.1006207.

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In this work, one dimensional Burgers' equation and coupled Burgers' equation are solved via Homotopy perturbation method (HPM). Solutions two and three-dimensional graphics and tables of some obtained results are constructed with the help of the computational program in the Wolfram Mathematica. All the solutions found in this study validate the efficiency of the method. According to the results, we have found out that our gained solutions convergence very speedily to the analytical solutions. In conclusion, we can say that the present method can also be applied for the solutions of a wide ran

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Yergaliyev, Madi, Tansholpan Sarybai, and Yrysdaulet Zhaksybay. "On the solvability of the Dirichlet problem for the viscous Burgers equation." Kazakh Mathematical Journal 24, no. 4 (2025): 22–36. https://doi.org/10.70474/f392sv46.

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In this work, we study a Dirichlet problem for the viscous Burgers equation in a domain with moving boundaries that degenerates at the initial moment. The primary method of investigation is the Galerkin method, for which we construct an orthonormal basis suitable for domains with moving boundaries. Uniform a priori estimates are obtained, and based on these, theorems on the unique solvability of the problem are proven using methods of functional analysis. The viscous Burgers equation serves asa simplified model for studying fundamental aspects of nonlinear systems. It bridges the gap between p

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Wazwaz, Abdul-Majid. "Multiple-front solutions for the Burgers equation and the coupled Burgers equations." Applied Mathematics and Computation 190, no. 2 (2007): 1198–206. http://dx.doi.org/10.1016/j.amc.2007.02.003.

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Fatima, N., and M. Dhariwal. "Solution of Nonlinear Coupled Burger and Linear Burgers Equation." International Journal of Engineering & Technology 7, no. 4.10 (2018): 670. http://dx.doi.org/10.14419/ijet.v7i4.10.21309.

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This paper applies an analytical technique, called Homotopy Perturbation Method to determine various problems of partial differential equations and coupled Burger equations in one and two dimension equations. The final conclusion confirms that the HPM is eventually useful as well as resourceful in predicting the explanation of these kind of problems and it further concludes that HPM could be a broad utilization in modern engineering complication.

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40

Ahmad, M. D. Al-Eybani. "The Differential Transform Method for Solving the Burgers Equation." International Journal of Mathematics and Physical Sciences Research 13, no. 1 (2025): 26–30. https://doi.org/10.5281/zenodo.15304250.

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<strong>Abstract:</strong> The Burgers equation is a fundamental partial differential equation (PDE) in applied mathematics, mathematical physics, and engineering, describing a variety of nonlinear wave phenomena such as fluid dynamics, gas dynamics, and traffic flow. Its nonlinear nature makes it a challenging yet fascinating problem to solve analytically or numerically. Among the various methods developed to tackle the Burgers equation, the Differential Transform Method (DTM) has emerged as a powerful semi-analytical technique due to its simplicity, computational efficiency, and ability to h

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Li, Lingxiao, Mingliang Wang, and Jinliang Zhang. "Application of Generalized Logistic Function to Travelling Wave Solutions for a Class of Nonlinear Evolution Equations." Mathematics 10, no. 21 (2022): 4017. http://dx.doi.org/10.3390/math10214017.

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The generalized Logistic function that solves a first-order nonlinear ODE with an arbitrary positive power term of the dependent variable is introduced in this paper, by means of which the traveling wave solutions of a class of nonlinear evolution equations, including the generalized Fisher equation, the generalized Nagumo equation, the generalized Burgers-Fisher equation, the generalized Gardner equation, the generalized KdV-Burgers equation, and the generalized Benney equation, are obtained successfully. In these particular cases, traveling wave solutions of several important model PDEs in m

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Yang, Hongwei, Baoshu Yin, Yunlong Shi, and Qingbiao Wang. "Forced ILW-Burgers Equation as a Model for Rossby Solitary Waves Generated by Topography in Finite Depth Fluids." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/491343.

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The paper presents an investigation of the generation, evolution of Rossby solitary waves generated by topography in finite depth fluids. The forced ILW- (Intermediate Long Waves-) Burgers equation as a model governing the amplitude of solitary waves is first derived and shown to reduce to the KdV- (Korteweg-de Vries-) Burgers equation in shallow fluids and BO- (Benjamin-Ono-) Burgers equation in deep fluids. By analysis and calculation, the perturbation solution and some conservation relations of the ILW-Burgers equation are obtained. Finally, with the help of pseudospectral method, the numer

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SHI, B. J., D. W. SHU, S. J. SONG, and Y. M. ZHANG. "SOLVING BURGERS EQUATION BY A MESHLESS METHOD." Modern Physics Letters B 19, no. 28n29 (2005): 1651–54. http://dx.doi.org/10.1142/s021798490501013x.

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Burgers equation is a fundamental partial differential equation of second order to describe the integrated process of convection-diffusion in physics. It occurs in various areas of applied mathematics and physics, such as modeling of turbulence, boundary layer behavior, shock wave formation, and mass transport. The convective and diffusive terms in Navier-Stokes equation are included in Burgers equation while the pressure term is neglected. A least-square point collocation meshless formula is proposed to discretize the Burgers equation. To verify the present meshless approach, the distribution

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Hwang, Seok. "Kinetic decomposition for the generalized BBM–Burgers equations with dissipative term." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 6 (2004): 1149–62. http://dx.doi.org/10.1017/s030821050000367x.

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We consider the generalized Benjamin–Bona–Mahony–Burgers (BBM–Burgers) equations with dissipative term. We establish the condition under which the solutions uα,β,γ converge in a strong topology to the entropy solution of a scalar conservation laws using methodology developed by Hwang and Tzavaras. First, we obtain the approximate transport equation for the given BBM–Burgers equations. Then, using the averaging lemma, we obtain the convergence.

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Alqahtani, Awatif Muflih. "Solution of the Generalized Burgers Equation Using Homotopy Perturbation Method with General Fractional Derivative." Symmetry 15, no. 3 (2023): 634. http://dx.doi.org/10.3390/sym15030634.

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This research paper introduces the generalized Burgers equation, a mathematical model defined using the general fractional derivative, the most recent operator in fractional calculus. The general fractional derivative can be reduced into three well-known operators, providing a more tractable form of the equation. We apply the homotopy perturbation method (HPM), a powerful analytical technique, to obtain the solution of the generalized Burgers equation. The results are illustrated using a practical example, and we present an analysis of the three reduced operators. In addition, a graphical anal

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Sakthivel, Rathinasamy, Changbum Chun, and Jonu Lee. "New Travelling Wave Solutions of Burgers Equation with Finite Transport Memory." Zeitschrift für Naturforschung A 65, no. 8-9 (2010): 633–40. http://dx.doi.org/10.1515/zna-2010-8-903.

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The nonlinear evolution equations with finite memory have a wide range of applications in science and engineering. The Burgers equation with finite memory transport (time-delayed) describes convection-diffusion processes. In this paper, we establish the new solitary wave solutions for the time-delayed Burgers equation. The extended tanh method and the exp-function method have been employed to reveal these new solutions. Further, we have calculated the numerical solutions of the time-delayed Burgers equation with initial conditions by using the homotopy perturbation method (HPM). Our results sh

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Joseph, Owuor Owino. "A GROUP APPROACH TO EXACT SOLUTIONS AND CONSERVATION LAWS OF BURGER'S EQUATION." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 10, no. 09 (2022): 2894–909. https://doi.org/10.5281/zenodo.7074684.

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A classical Burger’s equation is studied by symmetry analysis. The Lie point symmetries con- structed are applied in symmetry reductions and the resulting reduced systems investigated for exact group-invariant solutions. We also construct solitons using symmetry span of space and time translations. Finally, we prove that Burgers equation is a conservation law by the multiplier technique.

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Smaoui, Nejib. "Analyzing the dynamics of the forced Burgers equation." Journal of Applied Mathematics and Stochastic Analysis 13, no. 3 (2000): 269–85. http://dx.doi.org/10.1155/s1048953300000241.

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We study numerically the long-time dynamics of a system of reaction-diffusion equations that arise from the viscous forced Burgers equation (ut+uux−vuxx=F). A nonlinear transformation introduced by Kwak is used to embed the scalar Burgers equation into a system of reaction diffusion equations. The Kwak transformation is used to determine the existence of an inertial manifold for the 2-D Navier-Stokes equation. We show analytically as well as numerically that the two systems have a similar, long-time dynamical, behavior for large viscosity v.

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Miyazaki, Takeshi. "Diffusion equation coupled to Burgers' equation." Fluid Dynamics Research 2, no. 1 (1987): 25–33. http://dx.doi.org/10.1016/0169-5983(87)90015-3.

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Zhao, Qingli, Ruiwen Wang, Zhaoqing Wang, and Xiaoping Zhang. "Barycentric Rational Collocation Method for Burgers’ Equation." Journal of Mathematics 2022 (May 9, 2022): 1–14. http://dx.doi.org/10.1155/2022/2177998.

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In this article, barycentric rational collocation method is introduced to solve Burgers’ equation. The algebraic equations of the barycentric rational collocation method are presented. Numerical analysis and error estimates are established. With the help of the barycentric rational interpolation theory, the convergence rates of the barycentric rational collocation method for Burgers’ equation are proved. Numerical experiments are carried out to validate the convergence rates and show the efficiency.

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