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Lie symmetry analysis and invariant solutions for the(3+1)-dimensional Virasoro integrable model

Chinese Physics B 2023年第4期32卷 249-254页

作者：胡恒春李雅琦 College of Science University of Shanghai for Science and TechnologyShanghai 200093China

Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal *** solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.

关键词： (3+1)-dimensional Virasoro integrable model Lie symmetry invariant solutions

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Exhaustive Classification of the invariant solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition

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Communications in Theoretical Physics 2018年第5期69卷 477-505页

作者： Fatemeh Ahangari Department of Mathematics Faculty of Mathematical SciencesAlzahra University

Problems of thermodynamic phase transition originate inherently in solidification, combustion and various other significant fields. If the transition region among two locally stable phases is adequately narrow, the dynamics can be modeled by an interface motion. This paper is devoted to exhaustive analysis of the invariant solutions for a modified Kuramoto-Sivashinsky equation in two spatial and one temporal dimensions is presented. This nonlinear partial differential equation asymptotically characterizes near planar interfaces, which are marginally long-wave unstable. For this purpose, by applying the classical symmetry method for this model the classical symmetry operators are ***, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras, which yields the preliminary classification of group invariant solutions is constructed. Mainly, the Lie invariants corresponding to the infinitesimal symmetry generators as well as associated similarity reduced equations are also pointed out. Furthermore,the nonclassical symmetries of this nonlinear PDE are also comprehensively investigated.

关键词： phase transition modified Kuramoto-Sivashinsky ((2D) MKS) equation symmetries optimal system invariant solutions

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On New invariant solutions of Generalized Fokker-Planck Equation

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Communications in Theoretical Physics 2004年第5期41卷 665-668页

作者： YAORuo-Xia LIZhi-Bin DepartmentofComputerScience EastChinaNormalUniversityShanghai200062China

The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first repor... 详细信息

关键词： Fokker-Planck equation potential symmetry invariant solutions symbolic computation

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On Lie symmetries and invariant solutions of Broer-Kaup-Kupershmidt equation in shallow water of uniform depth

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Journal of Ocean Engineering and Science 2024年第3期9卷 199-206页

作者： Dig Vijay Tanwar Mukesh Kumar Department of Mathematics Graphic Era Deemed to be UniversityDehradun 248002India Department of Mathematics Motilal Nehru National Institute of Technology AllahabadPrayagraj 211004India

The dynamics of atmosphere and ocean can be examined under different circumstances of shallow water waves like shallow water gravity waves,Kelvin waves,Rossby waves and inertio-gravity *** influences of these waves describe the climate change adaptation on marine environment and ***,the present work aims to derive symmetry reductions of Broer-Kaup-Kupershmidt equation in shallow water of uniform depth and then a variety of exact solutions are *** represents the propagation of nonlinear and dispersive long gravity waves in two horizontal directions in shallow *** invariance of test equations under one parameter transformation leads to reduction of independent ***,twice implementations of symmetry method result into equivalent system of ordinary differential ***,the exact solutions of these ODEs are computed under parametric *** derive results entail several arbitrary constants and functions,which make the findings more *** on the appropriate choice of existing parameters,these solutions are supplemented numerically and show parabolic nature,intensive and non-intensive behavior of solitons.

关键词： BKK equation Lie symmetry method Invariance property invariant solutions Solitons

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Lie Symmetries,1-Dimensional Optimal System and Optimal Reductions of(1+2)-Dimensional Nonlinear Schrodinger Equation

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Journal of Applied Mathematics and Physics 2014年第7期2卷 603-620页

作者： Meirong Mu Chaolu Temuer Inner Mongolia University HohhotChina Shanghai Maritime University ShanghaiChina

For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, classical symmetry algebra is found and 1-dimensional optimal system, up to conjugacy, is constructed. Its symmetry reductions are performed for each... 详细信息

关键词： Nonlinear Schrodinger Equation Classical Symmetry Optimal System Symmetry Reductions invariant solutions

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On Symmetry Reduction of the (1 + 3)-Dimensional Inhomogeneous Monge-Ampère Equation to the First-Order ODEs

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Applied Mathematics 2020年第11期11卷 1178-1195页

作者： Vasyl M. Fedorchuk Volodymyr I. Fedorchuk Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine L'viv Ukraine

We present the results obtained concerning the classification of symmetry reduction of the (1 + 3)-dimensional inhomogeneous Monge-Ampère equation to first-order ODEs. Some classes of the invariant solutions are cons... 详细信息

关键词： Symmetry Reduction invariant solutions Monge-Ampère Equation Classification of Lie Algebras Poincaré Group P(1 4)

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