Relevant bibliographies by topics / Lie symmetry method

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Lie symmetry method'

Author: Grafiati
Published: 6 September 2023
Last updated: 31 July 2025

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Journal articles on the topic "Lie symmetry method"

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Zheng Mingliang. "Disturbance Decoupling for a Class of Nonlinear Control Systems Based on Lie Symmetry Method." Journal of Electrical Systems 20, no. 3 (2024): 3650–61. https://doi.org/10.52783/jes.5252.

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To fully explore the inherent structural properties of symmetric nonlinear control systems, this paper introduces the Lie symmetry method to the disturbance decoupling problem for a class of SISO nonlinear control systems. Firstly, the state-space equations and the disturbance decoupling model for a class of SISO nonlinear control systems are defined; Secondly, the key technologies and algorithm approaches of Lie symmetry theory for differential equations are introduced, and the conditions and the properties of Lie symmetry for nonlinear control systems under group action are given in detail;
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Ji, Lina, and Rui Wang. "Conditional Lie-Bäcklund Symmetries and Differential Constraints of Radially Symmetric Nonlinear Convection-Diffusion Equations with Source." Entropy 22, no. 8 (2020): 873. http://dx.doi.org/10.3390/e22080873.

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A conditional Lie-Bäcklund symmetry method and differential constraint method are developed to study the radially symmetric nonlinear convection-diffusion equations with source. The equations and the admitted conditional Lie-Bäcklund symmetries (differential constraints) are identified. As a consequence, symmetry reductions to two-dimensional dynamical systems of the resulting equations are derived due to the compatibility of the original equation and the additional differential constraint corresponding to the invariant surface equation of the admitted conditional Lie-Bäcklund symmetry.
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YU, JUN, and HANWEI HU. "FINITE SYMMETRY GROUP AND COHERENT SOLITON SOLUTIONS FOR THE BROER–KAUP–KUPERSHMIDT SYSTEM." International Journal of Bifurcation and Chaos 23, no. 09 (2013): 1350156. http://dx.doi.org/10.1142/s0218127413501563.

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A modified CK direct method is generalized to find finite symmetry groups of nonlinear mathematical physics systems. For the (2 + 1)-dimensional Broer–Kaup–Kupershmidt (BKK) system, both the Lie point symmetry and the non-Lie symmetry groups are obtained by this method. While using the traditional Lie approach, one can only find the Lie symmetry groups. Furthermore, abundant localized structures of the BKK equation are also obtained from the non-Lie symmetry group.
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Wang, Zhenli, Liangji Sun, Rui Hua, Lihua Zhang, and Haifeng Wang. "Lie Symmetry Analysis, Particular Solutions and Conservation Laws of Benjiamin Ono Equation." Symmetry 14, no. 7 (2022): 1315. http://dx.doi.org/10.3390/sym14071315.

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In this paper, by applying the Lie group method and the direct symmetry method, Lie algebras of the Benjiamin Ono equation are obtained, and we find that results of the two methods are same. Based on the Lie algebra, Lie symmetry groups, relationships between new solutions and old solutions, two kinds of ODEs as symmetry reductions are obtained. Making use of the power series method, the exact power series solution of the Benjiamin Ono equation has been derived. We also give the conservation laws of Benjiamin Ono equation by means of Ibragimovs new conservation Theorem.
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Li, Hongjie, Dandan Wang, and Mingliang Zheng. "Disturbance decoupling for biological fermentation systems with single input single output." Molecular & Cellular Biomechanics 21, no. 4 (2024): 847. https://doi.org/10.62617/mcb847.

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The biological fermentation process has the characteristics of nonlinearity and multivariable coupling. To improve the performance of decoupling control in the fermentation process, a disturbance decoupling control based on the Lie symmetry method is proposed to obtain the analytical feedback control for a class of biological fermentation systems with single input single output (SISO). Firstly, the state-space equations and the disturbance decoupling model for a class of SISO biological fermentation systems are defined; Secondly, the key technologies and algorithm approaches of Lie symmetry th
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Chen, Yong, and Xiaorui Hu. "Lie Symmetry Group of the Nonisospectral Kadomtsev-Petviashvili Equation." Zeitschrift für Naturforschung A 64, no. 1-2 (2009): 8–14. http://dx.doi.org/10.1515/zna-2009-1-202.

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The classical symmetry method and the modified Clarkson and Kruskal (C-K) method are used to obtain the Lie symmetry group of a nonisospectral Kadomtsev-Petviashvili (KP) equation. It is shown that the Lie symmetry group obtained via the traditional Lie approach is only a special case of the symmetry groups obtained by the modified C-K method. The discrete group analysis is given to show the relations between the discrete group and parameters in the ansatz. Furthermore, the expressions of the exact finite transformation of the Lie groups via the modified C-K method are much simpler than those
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Bilige, Sudao, and Yanqing Han. "Symmetry reduction and numerical solution of a nonlinear boundary value problem in fluid mechanics." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 3 (2018): 518–31. http://dx.doi.org/10.1108/hff-08-2016-0304.

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Purpose The purpose of this paper is to study the applications of Lie symmetry method on the boundary value problem (BVP) for nonlinear partial differential equations (PDEs) in fluid mechanics. Design/methodology/approach The authors solved a BVP for nonlinear PDEs in fluid mechanics based on the effective combination of the symmetry, homotopy perturbation and Runge–Kutta methods. Findings First, the multi-parameter symmetry of the given BVP for nonlinear PDEs is determined based on differential characteristic set algorithm. Second, BVP for nonlinear PDEs is reduced to an initial value problem
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Zhang, Bo, and Hengchun Hu. "Similarity Reduction and Exact Solutions of a Boussinesq-like Equation." Zeitschrift für Naturforschung A 73, no. 4 (2018): 357–62. http://dx.doi.org/10.1515/zna-2017-0442.

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AbstractThe similarity reduction and similarity solutions of a Boussinesq-like equation are obtained by means of Clarkson and Kruskal (CK) direct method. By using Lie symmetry method, we also obtain the similarity reduction and group invariant solutions of the model. Further, we compare the results obtained by the CK direct method and Lie symmetry method, and we demonstrate the connection of the two methods.
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Tian, Yi, and Kang-Le Wang. "Polynomial characteristic method an easy approach to lie symmetry." Thermal Science 24, no. 4 (2020): 2629–35. http://dx.doi.org/10.2298/tsci2004629t.

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Along the approach to Lie symmetry, it is always needed to solve an over-determined system, which is difficult and complex if not impossible. Here we suggest a new polynomial characteristic method combined with Lie algorithm to complete symmetry classification for a class of perturbed equations. A differential polynomial characteristic set algorithm is proposed to decompose the determining equations into a series of equations easy to be solved.
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Yang, Huizhang, Wei Liu, and Yunmei Zhao. "Lie Symmetry Analysis, Traveling Wave Solutions, and Conservation Laws to the (3 + 1)-Dimensional Generalized B-Type Kadomtsev-Petviashvili Equation." Complexity 2020 (October 24, 2020): 1–8. http://dx.doi.org/10.1155/2020/3465860.

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In this paper, the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili(BKP) equation is studied applying Lie symmetry analysis. We apply the Lie symmetry method to the (3 + 1)-dimensional generalized BKP equation and derive its symmetry reductions. Based on these symmetry reductions, some exact traveling wave solutions are obtained by using the tanh method and Kudryashov method. Finally, the conservation laws to the (3 + 1)-dimensional generalized BKP equation are presented by invoking the multiplier method.
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Dissertations / Theses on the topic "Lie symmetry method"

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Mehraban, Arash. "Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation." Digital Commons @ East Tennessee State University, 2010. https://dc.etsu.edu/etd/1736.

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In Reaction-Diffusion systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion equation that arises both in population genetics and in modeling the transmission of action potentials in the nervous system. In this paper we are interested in finding solutions to this equation. Using Lie groups in particular, we would like to find symmetries of the Fitzhugh Nagumo equation that reduce this non-linea
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DE, VECCHI FRANCESCO CARLO. "LIE SYMMETRY ANALYSIS AND GEOMETRICAL METHODS FOR FINITE AND INFINITE DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/565457.

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The main aim of the thesis is a systematic application (via suitable generalizations) of Lie symmetry analysis, or more generally, of the various geometric techniques for differential equations, to the study of finite and infinite dimensional stochastic differential equations (SDEs). The work can be divided in three main parts. In the first part a new geometric approach to finite dimensional SDEs driven by a multidimensional Brownian motion is proposed, which is based on a new notion of random transformations of a stochastic process called stochastic transformations. After having studied the
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Granström, Frida. "Symmetry methods and some nonlinear differential equations : Background and illustrative examples." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-48020.

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Differential equations, in particular the nonlinear ones, are commonly used in formulating most of the fundamental laws of nature as well as many technological problems, among others. This makes the need for methods in finding closed form solutions to such equations all-important. In this thesis we study Lie symmetry methods for some nonlinear ordinary differential equations (ODE). The study focuses on identifying and using the underlying symmetries of the given first order nonlinear ordinary differential equation. An extension of the method to higher order ODE is also discussed. Several illus
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Altafini, Claudio. "Geometric control methods for nonlinear systems and robotic applications." Doctoral thesis, Stockholm : Tekniska högsk, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3151.

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Семеген, Богдан Васильович, та Bohdan Semehen. "Метод підвищення криптостійкості симетричних алгоритмів шифрування". Master's thesis, Тернопільський національний технічний університет імені Івана Пулюя, 2021. http://elartu.tntu.edu.ua/handle/lib/36750.

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Мета цієї роботи полягає у розробці методу для підвищення криптостійксті симетричних алгоритмів шифрування та програмній його реалізації. У кваліфікаційній роботі проаналізовано симетричні алгоритми шифрування, що дало змогу визначити слабкі сторони їхнього застосування. Описано основні методи криптоаналізу, які можуть зробити шифри уразливими і становити загрозу розкриття відкритого тексту. Також було розглянуто способи генерації перестановок та створено новий алгоритм генерації унікальної перестановки. В роботі було розроблено метод підвищення криптостійкості на основі генерації унікальних
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Khojayori, Farahnoz N. "Floral symmetry genes elucidate the development and evolution of oil-bee pollinated flowers of Malpighiaceae and Krameriaceae." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5585.

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Specialization on insect and animal pollinators is thought to be the driving force for the evolution of floral traits. Specifically in the New World (NW), the oil-bee pollination syndrome has led to the convergence of floral characters in two distantly related families of core eudicots, Malpighiaceae and Krameriaceae. Both families display a flag-like structure that establishes a zygomorphic flower and floral oil rewards in epithelial elaiophores. These traits work concomitantly to attract and reward female oil-bees that help fertilize these flowers and in return receive oils. The underlying g
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Kundu, Bidisha. "On the analysis of axially loaded Euler-Bernoulli beam using Galerkin, Fourier transform, and Lie symmetry approach." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/5244.

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The beam with axial load is one of the fundamental models in the field of physics and engineering. The applications of this model span from a guitar string to the rotating blade of a helicopter. It has an important role in vibration theory and structural mechanics. Also, it establishes a relationship between the mathematical continuum concept and continuum mechanics as it is the most basic example of a continuum physical model. For the long and slender beams, the Euler-Bernoulli beam theory is used. In this thesis, Euler-Bernoulli beam with axial load is studied. For the wide application
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Yeh, Po-Kai, and 葉柏開. "Application of Lie Symmetry Analysis and Method of Generating Integrals of Motion to Third Order Emden-Fowler Equations." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/79023777230158728006.

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碩士<br>國立嘉義大學<br>應用數學系研究所<br>95<br>In this thesis, we use Lie symmetry analysis and the method of generating integrals of motion to find the general solutions or the first integrals of the third order Emden-Fowler equations. We also reduce some of the equations to lower order ODEs, through the method of canonical coordinates and the method of differential invariants.
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Lamothe, Vincent. "Analyse de groupe d’un modèle de la plasticité idéale planaire et sur les solutions en termes d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre." Thèse, 2013. http://hdl.handle.net/1866/10343.

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Les objets d’étude de cette thèse sont les systèmes d’équations quasilinéaires du premier ordre. Dans une première partie, on fait une analyse du point de vue du groupe de Lie classique des symétries ponctuelles d’un modèle de la plasticité idéale. Les écoulements planaires dans les cas stationnaire et non-stationnaire sont étudiés. Deux nouveaux champs de vecteurs ont été obtenus, complétant ainsi l’algèbre de Lie du cas stationnaire dont les sous-algèbres sont classifiées en classes de conjugaison sous l’action du groupe. Dans le cas non-stationnaire, une classification des algèbres de Lie a
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Khosravian, Alireza. "State Estimation for Systems on Lie Groups with Nonideal Measurements." Phd thesis, 2016. http://hdl.handle.net/1885/109348.

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This thesis considers the state estimation problem for invariant systems on Lie groups with inputs in its associated Lie algebra and outputs in homogeneous spaces of the Lie group. A particular focus of this thesis is the development of state estimation methodologies for systems with nonideal measurements, especially systems with additive input measurement bias, output measurement delay, and sampled outputs. The main contribution of the thesis is to effectively employ the symmetries of the system dynamics and to benefit from the Lie group structure of th
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Books on the topic "Lie symmetry method"

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1943-, Bluman George W., ed. Symmetry and integration methods for differential equations. Springer, 2002.

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Jürgen, Fuchs. Symmetries, lie algebras and representations: A graduate course for physicists. Cambridge University Press, 1997.

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Jürgen, Fuchs. Symmetries, lie algebras and representations: A graduate course for physicists. Cambridge University Press, 2003.

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Advanced Symmetry Method Differential Equations (Applied Mathematical Sciences). Springer, 2007.

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Rouvière, François. Symmetric Spaces and the Kashiwara-Vergne Method. Springer London, Limited, 2014.

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Rouvière, François. Symmetric Spaces and the Kashiwara-Vergne Method. Springer, 2014.

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Symmetry breaking. 2nd ed. Springer, 2008.

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Fuchs, Jürgen, and Christoph Schweigert. Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists (Cambridge Monographs on Mathematical Physics). Cambridge University Press, 1997.

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Book chapters on the topic "Lie symmetry method"

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Mishra, Shivam Kumar. "Soliton Solutions of (2+1)-Dimensional Modified Calogero-Bogoyavlenskii-Schiff (mCBS) Equation by Using Lie Symmetry Method." In Lecture Notes in Electrical Engineering. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-1824-7_13.

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Baldeaux, Jan, and Eckhard Platen. "Lie Symmetry Group Methods." In Functionals of Multidimensional Diffusions with Applications to Finance. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00747-2_4.

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Baldeaux, Jan, and Eckhard Platen. "Transition Densities via Lie Symmetry Methods." In Functionals of Multidimensional Diffusions with Applications to Finance. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00747-2_5.

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Qadir, Asghar, and Fazal M. Mahomed. "Complex Methods for Lie Symmetry Analysis." In Nonlinear Physical Science. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-4683-6_4.

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Vassilev, Vassil M., Petar A. Djondjorov, and Ivaïlo M. Mladenov. "Lie Group Analysis of the Willmore and Membrane Shape Equations." In Similarity and Symmetry Methods. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08296-7_7.

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Rouvière, François. "The Kashiwara-Vergne Method for Lie Groups." In Symmetric Spaces and the Kashiwara-Vergne Method. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09773-2_1.

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Shelepin, A. L., and L. A. Shelepin. "Symmetric Basis in Lie Group Representation Theory and Constructing Clebsch-Gordon Coefficients." In Group Theoretical Methods in Physics. Volume II. CRC Press, 2024. http://dx.doi.org/10.1201/9781003580850-13.

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Kaur, Lakhveer, K. Murugesan, and Aman Fatima. "Unveiling Dynamics of Solutions for Variable Killing Rate Brain Tumor Model With Lie Symmetry Analysis." In Advances in Mathematics: Theory, Methods & Applications. River Publishers, 2025. https://doi.org/10.1201/9788770046701-8.

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Johansson, Arne V., Björn Lindgren, and Jens M. Österlund. "Experimental Tests of Mean Velocity Distribution Laws Derived by Lie Group Symmetry Methods in Turbulent Boundary Layers." In IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-94-007-0997-3_45.

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Iliopoulos, J., and T. N. Tomaras. "Elements of Group Theory." In Elementary Particle Physics. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192844200.003.0005.

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The mathematical language which encodes the symmetry properties in physics is group theory. In this chapter we recall the main results. We introduce the concepts of finite and infinite groups, that of group representations and the Clebsch–Gordan decomposition. We study, in particular, Lie groups and Lie algebras and give the Cartan classification. Some simple examples include the groups U(1), SU(2) – and its connection to O(3) – and SU(3). We use the method of Young tableaux in order to find the properties of products of irreducible representations. Among the non-compact groups we focus on the
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Conference papers on the topic "Lie symmetry method"

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Mavuri, Satya P., Simon Watkins, and Jon Watmuff. "A Novel Mirror-Image Technique for Wheel and Ground Simulation in Automotive Wind-Tunnels." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77102.

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A novel method for simulating the relative motions of the wheels and moving ground for road vehicle aerodynamics is presented. The method revisits an old concept where two identical vehicles are used and positioned so that they are mirror images, with the ground being represented by the horizontal plane of symmetry. The method involves double symmetry, where two half models (e.g. a car split down the vertical centerline) contact at the rotating wheel contact patches and the resulting (opened) vehicle halves lie on a reflection plane. This can either be the tunnel floor or the equivalent CFD pl
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Reinhardt, Wolf. "Effect of Plane Strain, Plane Stress and Bending on Equivalent Solid Collapse Predictions for Perforated Plates." In ASME 2002 Pressure Vessels and Piping Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/pvp2002-1303.

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An equivalent solid based method of predicting the plastic (limit) collapse of perforated plates has been developed in the recent literature. Higher order collapse surfaces with suitable symmetry properties are used for the analysis. The equation for the collapse surface contains a number of constants that are determined by comparison to a Finite Element analysis of an actual perforated periodic cell subject to selected membrane states of stress. Using a typical triangular perforation pattern, the present paper investigates the effect of simplifying assumptions that were made during the period
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Honda, Tomonori, Fabien Nicaise, and Erik K. Antonsson. "Synthesis of Structural Symmetry Driven by Cost Savings." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85111.

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An engineer presented with a design challenge often creates a symmetric solution. For instance, consider a table (front-back and left-right symmetry), a car (left and right symmetry), a bridge (front-back and left-right symmetry), or the space shuttle (left-right) symmetry. These examples may not be 100% symmetric, but their overriding features are remarkably similar. The reasons for the design of symmetric structures is not always clear. In some cases, like the table, symmetry may be a tradition. Similarly, the symmetry may be for aesthetic reasons. However in automated design algorithms, esp
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Muriel, C., J. L. Romero, and A. Ruiz. "Integration methods for equations without enough Lie point symmetries." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125078.

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Changizi, M. Amin, Ali Abolfathi, and Ion Stiharu. "MEMS Wind Speed Sensor: Large Deflection of Curved Micro-Cantilever Beam Under Uniform Horizontal Force." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50560.

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Micro-cantilever beams are currently employed as sensor in various fields. Of main applications, is using such beams in wind speed sensors. For this purpose, curved out of plane micro-cantilever beams are used. Uniform pressure on such beams causes a large deflection of beam. General mechanics of material theory deals with small deflection and thus cannot be used for explaining this deflection. Although there are a body of works on analysing of large deflection [1], nonlinear deflection, of curved beams [2], yet there is no research on large deflection of curved beam under horizontal uniform d
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Changizi, M. Amin, and Ion Stiharu. "A Complete Parametric Study of Pull-In Voltage by Nonlinear Differential Equation." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37744.

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Micro-cantilever beams are interested structures in MEMS because of their fabrication is very easy and its versatility. The importance of micro-cantilevers beam in MEMS has driven various investigations like static and dynamic performances under different loading such as potential fields. In this research the non-linear differential equation which models dynamics of a micro-cantilever beams vibration subjected to electrostatic field has been studied. The model which has one degree of freedom is used to calculate the pull-in voltage. This model adopted based on different method of calculating s
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Ahasan, Kawkab, and Jong-Hoon Kim. "Study of Angle-of-Attack (AoA) for Airfoil in Deterministic Lateral Displacement (DLD)." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-11708.

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Abstract Deterministic lateral displacement (DLD) is a method of inertial size-based particle separation with potential applications in high throughput sample processing, such as the fractionation of blood or the purification of target species like viral particles or circulating tumor cells. Recently, it has been shown that symmetric airfoils with neutral angle-of-attack (AoA) can be used for high-throughput design of DLD device, due to their mitigation of vortex effects and preservation of flow symmetry under high Reynolds number (Re) conditions. While high-Re operation with symmetric airfoil
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Barion, A., M. J. H. Anthonissen, J. H. M. ten Thije Boonkkamp, and W. L. Ijzerman. "Lie algebraic methods for aberrations of plane-symmetric mirror systems." In International Optical Design Conference 2023, edited by David M. Aikens, Henning Rehn, Simon Thibault, and Kristina Uhlendorf. SPIE, 2023. http://dx.doi.org/10.1117/12.2692554.

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Lindgren, B., J. Osterlund, and A. Johansson. "Evaluation of scaling laws derived from lie group symmetry methods in turbulent boundary layers." In 40th AIAA Aerospace Sciences Meeting & Exhibit. American Institute of Aeronautics and Astronautics, 2002. http://dx.doi.org/10.2514/6.2002-1103.

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Striebel, Michael, Michael Günther, Francesco Knechtli, and Michele Wandelt. "Symmetric Partitioned Runge-Kutta Methods for Differential Equations on Lie-Groups." In XXIX International Symposium on Lattice Field Theory. Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.139.0049.

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