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Journal articles on the topic 'Boussinesq equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Dutykh, Denys, and Frédéric Dias. "Dissipative Boussinesq equations." Comptes Rendus Mécanique 335, no. 9-10 (2007): 559–83. http://dx.doi.org/10.1016/j.crme.2007.08.003.

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2

Zou, Z. L. "Higher order Boussinesq equations." Ocean Engineering 26, no. 8 (1999): 767–92. http://dx.doi.org/10.1016/s0029-8018(98)00019-5.

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3

Morimoto, Hiroko. "On non-stationary boussinesq equations." Proceedings of the Japan Academy, Series A, Mathematical Sciences 67, no. 5 (1991): 159–61. http://dx.doi.org/10.3792/pjaa.67.159.

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4

Kennedy, Andrew B., James T. Kirby, and Mauricio F. Gobbi. "Simplified higher-order Boussinesq equations." Coastal Engineering 44, no. 3 (2002): 205–29. http://dx.doi.org/10.1016/s0378-3839(01)00032-1.

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5

Gao, Yi-Tian, and Bo Tian. "On the Variant Boussinesq Equations." Zeitschrift für Naturforschung A 52, no. 4 (1997): 335–36. http://dx.doi.org/10.1515/zna-1997-0406.

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6

Shakhmurov, Veli B. "Nonlocal problems for Boussinesq equations." Nonlinear Analysis 142 (September 2016): 134–51. http://dx.doi.org/10.1016/j.na.2016.04.014.

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7

Ma, Wen-Xiu, and Aslı Pekcan. "Uniqueness of the Kadomtsev-Petviashvili and Boussinesq Equations." Zeitschrift für Naturforschung A 66, no. 6-7 (2011): 377–82. http://dx.doi.org/10.1515/zna-2011-6-701.

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The Kadomtsev-Petviashvili and Boussinesq equations (uxxx -6uux)x -utx ±uyy = 0; (uxxx - 6uux)x +uxx ±utt = 0; are completely integrable, and in particular, they possess the three-soliton solution. This article aims to expose a uniqueness property of the Kadomtsev-Petviashvili (KP) and Boussinesq equations in the integrability theory. It is shown that the Kadomtsev-Petviashvili and Boussinesq equations and their dimensional reductions are the only integrable equations among a class of generalized Kadomtsev-Petviashvili and Boussinesq equations (ux1x1x1 - 6uux1 )x1 + ΣMi;j=1aijuxixj = 0; where

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8

Fan, En Gui, and Man Wai Yuen. "Similarity reductions and exact solutions for two-dimensional Euler–Boussinesq equations." Modern Physics Letters B 33, no. 27 (2019): 1950328. http://dx.doi.org/10.1142/s0217984919503287.

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In this paper, by introducing a stream function and new coordinates, we transform classical Euler–Boussinesq equations into a vorticity form. We further construct traveling wave solutions and similarity reduction for the vorticity form of Euler–Boussinesq equations. In fact, our similarity reduction provides a kind of linearization transformation of Euler–Boussinesq equations.

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9

Li, Biao, and Yong Chen. "Nonlinear Partial Differential Equations Solved by Projective Riccati Equations Ansatz." Zeitschrift für Naturforschung A 58, no. 9-10 (2003): 511–19. http://dx.doi.org/10.1515/zna-2003-9-1007.

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Based on the general projective Riccati equations method and symbolic computation, some new exact travelling wave solutions are obtained for a nonlinear reaction-diffusion equation, the highorder modified Boussinesq equation and the variant Boussinesq equation. The obtained solutions contain solitary waves, singular solitary waves, periodic and rational solutions. From our results, we can not only recover the known solitary wave solutions of these equations found by existing various tanh methods and other sophisticated methods, but also obtain some new and more general travelling wave solution

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10

Zhou, Yong, та Jishan Fan. "On the Cauchy problems for certain Boussinesq-α equations". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, № 2 (2010): 319–27. http://dx.doi.org/10.1017/s0308210509000122.

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We study the Cauchy problem of certain Boussinesq-α equations in n dimensions with n = 2 or 3. We establish regularity for the solution under ▽u ∈ L1 (0, T; Ḃ0∞,∞(ℝn)). As a corollary, the smooth solution of the Leray-α–Boussinesq system exists globally, when n = 2. For the Lagrangian averaged Boussinesq equations, a regularity criterion ▽θ ∈ L1(0, T;L∞(ℝ2)) is established. Other Boussinesq systems with partial viscosity are also discussed in the paper.

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11

Mhlanga, Isaiah Elvis, and Chaudry Masood Khalique. "Exact Solutions of Generalized Boussinesq-Burgers Equations and (2+1)-Dimensional Davey-Stewartson Equations." Journal of Applied Mathematics 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/389017.

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We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and (2+1)-dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the (2+1)-dimensional Davey-Stewartson equations.

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12

Lefter, Adriana-Ioana. "On the Feedback Stabilization of Boussinesq Equations." Annals of the Alexandru Ioan Cuza University - Mathematics 57, no. 2 (2011): 285–310. http://dx.doi.org/10.2478/v10157-011-0027-y.

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On the Feedback Stabilization of Boussinesq Equations This paper provides feedback stabilization results, preserving the invariance of a given convex set, for the Boussinesq system, in 2D and 3D. The proofs use an existence theorem for weak solutions.

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13

Ike, CC, HN Onah, and CU Nwoji. "BESSEL FUNCTIONS FOR AXISYMMETRIC ELASTICITY PROBLEMS OF THE ELASTIC HALF SPACE SOIL: A POTENTIAL FUNCTION METHOD." Nigerian Journal of Technology 36, no. 3 (2017): 773–81. http://dx.doi.org/10.4314/njt.v36i3.16.

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Elasticity problems are formulated using displacement methods or stress methods. In this paper a displacement formulation of axisymmetric elasticity problem is presented. The formulation uses the Boussinesqâ€“ Papkovich â€“ Neuber potential function. The problem is then solved by assuming Boussinesq â€“ Papkovich - Neuber potential functions in the form of Bessel functions of order zero and of the first kind. The potential functions are then made to satisfy the governing field equations and the associated boundary conditions for the particular problem of a point load at the origin of the semi-

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14

Xu, Fei, Yixian Gao, Xue Yang, and He Zhang. "Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method." Mathematical Problems in Engineering 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/5492535.

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This paper is aimed at constructing fractional power series (FPS) solutions of time-space fractional Boussinesq equations using residual power series method (RPSM). Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with initial value problems inRn. Using RPSM, we can obtain FPS solutions of fourth-, sixth-, and 2nth-order time-space fractional Boussinesq equations inRand fourth-order time-space fractional Boussinesq equations inR2andRn. Finally, by numerical experiments, it is shown that RPSM is a simple, effective,

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15

SAITO, Jun-ichi. "BOUSSINESQ EQUATIONS IN THIN SPHERICAL DOMAINS." Kyushu Journal of Mathematics 59, no. 2 (2005): 443–65. http://dx.doi.org/10.2206/kyushujm.59.443.

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16

Huang, Jianhua, Tianlong Shen, and Yuhong Li. "Dynamics of stochastic fractional Boussinesq equations." Discrete & Continuous Dynamical Systems - B 20, no. 7 (2015): 2051–67. http://dx.doi.org/10.3934/dcdsb.2015.20.2051.

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17

Engelbrecht, Jüri, Tanel Peets, and Kert Tamm. "Solitons modelled by Boussinesq-type equations." Mechanics Research Communications 93 (October 2018): 62–65. http://dx.doi.org/10.1016/j.mechrescom.2017.05.008.

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18

You, Yuncheng. "Global dynamics of 2D boussinesq equations." Nonlinear Analysis: Theory, Methods & Applications 30, no. 7 (1997): 4643–54. http://dx.doi.org/10.1016/s0362-546x(96)00218-0.

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19

Hamdi, S., W. H. Enright, Y. Ouellet, and W. E. Schiesser. "Exact Solutions of Extended Boussinesq Equations." Numerical Algorithms 37, no. 1-4 (2004): 165–75. http://dx.doi.org/10.1023/b:numa.0000049464.45146.88.

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20

TAO, Tao, and Liqun ZHANG. "Hölder continuous solutions Of Boussinesq equations." Acta Mathematica Scientia 38, no. 5 (2018): 1591–616. http://dx.doi.org/10.1016/s0252-9602(18)30834-8.

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21

LIU, Hanbing, and Haijun XIAO. "Boundary feedback stabilization of Boussinesq equations." Acta Mathematica Scientia 38, no. 6 (2018): 1881–902. http://dx.doi.org/10.1016/s0252-9602(18)30853-1.

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22

Gomes, Diogo A., and Claudia Valls. "Approximation of ill-posed boussinesq equations." Dynamical Systems 19, no. 4 (2004): 345–57. http://dx.doi.org/10.1080/1468936042000269587.

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23

Jabbari, A., H. Kheiri, and A. Bekir. "Analytical solution of variant Boussinesq equations." Mathematical Methods in the Applied Sciences 37, no. 6 (2013): 931–36. http://dx.doi.org/10.1002/mma.2853.

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24

Teng, Michelle H. "Solitary Wave Solution to Boussinesq Equations." Journal of Waterway, Port, Coastal, and Ocean Engineering 123, no. 3 (1997): 138–41. http://dx.doi.org/10.1061/(asce)0733-950x(1997)123:3(138).

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25

Baron-Pertuz, Cristian-Fabian, Ana-Magnolia Marin-Ramirez, and Ruben-Dario Ortiz-Ortiz. "An approximation to the Boussinesq equations." International Journal of Mathematical Analysis 8 (2014): 2433–37. http://dx.doi.org/10.12988/ijma.2014.48274.

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26

Karch, Grzegorz, and Nicolas Prioux. "Self-similarity in viscous Boussinesq equations." Proceedings of the American Mathematical Society 136, no. 03 (2007): 879–89. http://dx.doi.org/10.1090/s0002-9939-07-09063-6.

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27

Karasu, Atalay, and Arthemy V. Kiselev. "Gardner's deformations of the Boussinesq equations." Journal of Physics A: Mathematical and General 39, no. 37 (2006): 11453–60. http://dx.doi.org/10.1088/0305-4470/39/37/008.

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28

Scarpellini, B., and W. von Wahl. "Stability properties of the Boussinesq equations." Zeitschrift für angewandte Mathematik und Physik 49, no. 2 (1998): 294. http://dx.doi.org/10.1007/s000330050220.

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29

Schäffer, Hemming A., and Per A. Madsen. "Further enhancements of Boussinesq-type equations." Coastal Engineering 26, no. 1-2 (1995): 1–14. http://dx.doi.org/10.1016/0378-3839(95)00017-2.

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30

Meletlidou, Efi, Joël Pouget, Gérard Maugin, and Elias Aifantis. "Invariant relations in Boussinesq-type equations." Chaos, Solitons & Fractals 22, no. 3 (2004): 613–25. http://dx.doi.org/10.1016/j.chaos.2004.02.007.

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31

Cai, Xiao-jing, Chun-yan Xue, Xian-jin Li, Ying Liu, and Quan-sen Jiu. "Some remarks on planar Boussinesq equations." Acta Mathematicae Applicatae Sinica, English Series 28, no. 3 (2012): 525–34. http://dx.doi.org/10.1007/s10255-012-0167-1.

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32

Huang, Jianhua, Yuhong Li, and Jinqiao Duan. "Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/653160.

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This paper is devoted to the investigation of random dynamics of the stochastic Boussinesq equations driven by Lévy noise. Some fundamental properties of a subordinator Lévy process and the stochastic integral with respect to a Lévy process are discussed, and then the existence, uniqueness, regularity, and the random dynamical system generated by the stochastic Boussinesq equations are established. Finally, some discussions on the global weak solution of the stochastic Boussinesq equations driven by general Lévy noise are also presented.

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33

IVANOV, E., S. KRIVONOS, and R. P. MALIK. "BOUSSINESQ-TYPE EQUATIONS FROM NONLINEAR REALIZATIONS OF W3." International Journal of Modern Physics A 08, no. 18 (1993): 3199–222. http://dx.doi.org/10.1142/s0217751x93001284.

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We construct new coset realizations of infinite-dimensional linear [Formula: see text] symmetry associated with Zamolodchikov's W3 algebra which are different from the previously explored sl3 Toda realizations of [Formula: see text]. We deduce the Boussinesq and modified Boussinesq equations as constraints on the geometry of the corresponding coset manifolds. The main characteristic features of these realizations are: (i) among the coset parameters there are space and time coordinates x and t which enter the Boussinesq equations; all other coset parameters are regarded as fields depending on t

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34

Abazari, Reza, and Adem Kılıçman. "Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/468206.

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This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011) and (Kılıcman and Abazari, 2012), that focuses on the application ofG′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientistJoseph Valentin Boussinesq(1842–1929) described in the 1870s model equations for the propagation of long waves on the surfa

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35

Clarkson, Peter A. "New exact solutions of the Boussinesq equation." European Journal of Applied Mathematics 1, no. 3 (1990): 279–300. http://dx.doi.org/10.1017/s095679250000022x.

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In this paper new exact solutions are derived for the physically and mathematically significant Boussinesq equation. These are obtained in two different ways: first, by generating exact solutions to the ordinary differential equations which arise from (classical and nonclassical) similarity reductions of the Boussinesq equation (these ordinary differential equations are solvable in terms of the first, second and fourth Painlevé equations); and second, by deriving new space-independent similarity reductions of the Boussinesq equation. Extensive sets of exact solutions for both the second and fo

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36

Dutykh, D., and H. Kalisch. "Boussinesq modeling of surface waves due to underwater landslides." Nonlinear Processes in Geophysics 20, no. 3 (2013): 267–85. http://dx.doi.org/10.5194/npg-20-267-2013.

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Abstract. Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion that govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the Boussinesq scaling, with time-dependent bathymetry. A numerical model for the Boussinesq equations is introduced that is able to handle time-dependent bottom topography, and the equations of motion for the landslide and surface waves are

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37

CLARKSON, PETER A. "RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION." Analysis and Applications 06, no. 04 (2008): 349–69. http://dx.doi.org/10.1142/s0219530508001250.

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Rational solutions of the Boussinesq equation are expressed in terms of special polynomials associated with rational solutions of the second and fourth Painlevé equations, which arise as symmetry reductions of the Boussinesq equation. Further generalized rational solutions of the Boussinesq equation, which involve an infinite number of arbitrary constants, are derived. The generalized rational solutions are analogs of such solutions for the Korteweg–de Vries and nonlinear Schrödinger equations.

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38

de Szoeke, Roland A., and Roger M. Samelson. "The Duality between the Boussinesq and Non-Boussinesq Hydrostatic Equations of Motion." Journal of Physical Oceanography 32, no. 7 (2002): 2194–203. http://dx.doi.org/10.1175/1520-0485(2002)032<2194:tdbtba>2.0.co;2.

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39

Jafari, H., A. Borhanifar, and S. A. Karimi. "New solitary wave solutions for the bad Boussinesq and good Boussinesq equations." Numerical Methods for Partial Differential Equations 25, no. 5 (2008): 1231–37. http://dx.doi.org/10.1002/num.20400.

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40

Wei, Ge, James T. Kirby, Stephan T. Grilli, and Ravishankar Subramanya. "A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves." Journal of Fluid Mechanics 294 (July 10, 1995): 71–92. http://dx.doi.org/10.1017/s0022112095002813.

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Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlinearity is made, the equations can be applied to simulate strong wave interactions prior to wave breaking. A high-order numerical model based on the equations is developed and applied to the study of two

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41

Melinand, Benjamin. "Long wave approximation for water waves under a Coriolis forcing and the Ostrovsky equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 6 (2018): 1201–37. http://dx.doi.org/10.1017/s0308210518000136.

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This paper is devoted to the study of the long wave approximation for water waves under the influence of the gravity and a Coriolis forcing. We start by deriving a generalization of the Boussinesq equations in one (spatial) dimension and we rigorously justify them as an asymptotic model of water wave equations. These new Boussinesq equations are not the classical Boussinesq equations: a new term due to the vorticity and the Coriolis forcing appears that cannot be neglected. We study the Boussinesq regime and derive and fully justify different asymptotic models when the bottom is flat: a linear

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42

Michael Mueller, Thomas. "The Boussinesq Debate: Reversibility, Instability, and Free Will." Science in Context 28, no. 4 (2015): 613–35. http://dx.doi.org/10.1017/s0269889715000290.

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ArgumentIn 1877, a young mathematician named Joseph Boussinesq presented amémoireto theAcadémiedes sciences which demonstrated that some differential equations may have more than one solution. Boussinesq linked this fact to indeterminism and to a possible solution to the free will versus determinism debate. Boussinesq's main interest was to reconcile his philosophical and religious views with science by showing that matter and motion do not suffice to explain all there is in the world. His argument received mixed criticism that addressed both his philosophical views and the scientific content

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43

IVANOV, E., S. KRIVONOS, and R. P. MALIK. "N = 2 SUPER W3 ALGEBRA AND N = 2 SUPER BOUSSINESQ EQUATIONS." International Journal of Modern Physics A 10, no. 02 (1995): 253–88. http://dx.doi.org/10.1142/s0217751x95000127.

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We study classical N=2 super W3 algebra and its interplay with N=2 supersymmetric extensions of the Boussinesq equation in the framework of the nonlinear realization method and the inverse Higgs-covariant reduction approach. These techniques have been previously used by us in the bosonic W3 case to give a new geometric interpretation of the Boussinesq hierarchy. Here we deduce the most general N=2 super Boussinesq equation and two kinds of the modified N=2 super Boussinesq equations, as well as the super Miura maps relating these systems to each other, by applying the covariant reduction to ce

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44

Yang, Zonghang, and Benny Y. C. Hon. "An Improved Modified Extended tanh-Function Method." Zeitschrift für Naturforschung A 61, no. 3-4 (2006): 103–15. http://dx.doi.org/10.1515/zna-2006-3-401.

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In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type,Weierstrass elliptic doubly periodic type, triangular type and solitary wave solutions

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45

Erbay, H. A., S. Erbay, and A. Erkip. "Derivation of Generalized Camassa-Holm Equations from Boussinesq-type Equations." Journal of Nonlinear Mathematical Physics 23, no. 3 (2016): 314–22. http://dx.doi.org/10.1080/14029251.2016.1199493.

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46

Nargund, Achala, R. Madhusudhan, and S. B. Sathyanarayana. "HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS." JOURNAL OF ADVANCES IN PHYSICS 10, no. 3 (2015): 2825–33. http://dx.doi.org/10.24297/jap.v10i3.1322.

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In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysisÂ method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-SykesÂ plot for the region of convergence. We have applied Pade for the HAM series to identify theÂ singularity and reflect it in the graph. The HAM is a analytical technique which is used toÂ solve non-linear problems to generate a convergent series. HAM gives complete freedom toÂ choose the initial approximation of the solution, it is the auxilia

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47

Sharifi, Morteza, and Behruz Raesi. "Vortex Theory for Two Dimensional Boussinesq Equations." Applied Mathematics and Nonlinear Sciences 5, no. 2 (2020): 67–84. http://dx.doi.org/10.2478/amns.2020.2.00014.

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AbstractIn this paper, the single center vortex method (SCVM) is extended to find some vortex solutions of finite core size for dissipative 2D Boussinesq equations. Solutions are expanded in to series of Hermite eigenfunctions. After confirmation the convergence of series of the solution, we show that, by considering the effect of temperature on the evolution of the vortex for the same initial condition as in [19] the symmetry of the vortex destroyed rapidly.

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48

Li, Xiangzheng, Baoan Li, Jinlan Chen, and Mingliang Wang. "Exact Solutions to the Boussinesq-Burgers Equations." Journal of Applied Mathematics and Physics 05, no. 09 (2017): 1720–24. http://dx.doi.org/10.4236/jamp.2017.59145.

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49

Hsia, Chun-Hsiung, Tian Ma, and Shouhong Wang. "Rotating Boussinesq equations: Dynamic stability and transitions." Discrete & Continuous Dynamical Systems - A 28, no. 1 (2010): 99–130. http://dx.doi.org/10.3934/dcds.2010.28.99.

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50

Haussermann, John, and Robert A. Van Gorder. "Asymptotic solutions for singularly perturbed Boussinesq equations." Applied Mathematics and Computation 218, no. 20 (2012): 10238–43. http://dx.doi.org/10.1016/j.amc.2012.04.001.

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