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symmetry reduction of (2+1)-Dimensional Lax–Kadomtsev–Petviashvili Equation

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Communications in Theoretical Physics 2015年第2期63卷 136-140页

作者：胡恒春王竞博朱海东 College of Science University of Shanghai for Science and Technology National Laboratory of High Power Laser and Physics Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences

he Lax-Kadomtsev-Petviashvili equation is derived from the Lax fifth order equation, which is an important mathematical model in fluid physics and quantum field theory. symmetry reductions of the Lax-Kadomtsev- Petviashvili equation are studied by the means of the Clarkson-Kruskal direct method and the corresponding reduction equations are solved directly with arbitrary constants and functions.

关键词： Clarkson-Kruskal direct method Lax-Kadomtsev-Petviashvili equation symmetry reduction exact solution

symmetry reduction of Initial-Value Problems for a Class of Third-order Evolution Equations

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Communications in Theoretical Physics 2009年第7期52卷 55-59页

作者： LI Ji-Na FENG Wei QI Xin-Lei ZHANG Shun-Li Center for Nonlinear Studies Department of Mathematics Northwest University Xi＇an 710069 China Center of Nonlinear Science Ningbo University Ningbo 315211 China

symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is *** reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie *** classification theorems are obtained and some examples are taken to show the main reduction procedure.

关键词： symmetry reduction third-order evolution equation Cauchy problem

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)

Lie symmetry analysis and reduction of a new integrable coupled KdV system

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Chinese Physics B 2007年第2期16卷 303-309页

作者：钱素平田立新 Department of Mathematics Changshu Institute of Technology Changshu 215500 China Nonlinear Scientific Research Center Faculty of ScienceJiangsu University Zhenjiang 212013 China

In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg-de Vries （KdV） equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invarlant solution of reduced equations can be acquired by means of the Painlevé I transcendent function.

关键词： the coupled KdV equations symmetry reduction group-invariant solutions

Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions

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Chinese Physics B 2024年第3期33卷 150-159页

作者：陈孜童贾曼郝夏芝楼森岳 School of Mathematics and Statistics Ningbo UniversityNingbo 315211China School of Physical Science and Technology Ningbo UniversityNingbo 315211China College of Science Zhejiang University of TechnologyHangzhou 310014China

Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV ***,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO *** the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.

关键词： Kadomtsev-Petviashvili(KP)equation decomposition Bäcklund transformation symmetry reduction

symmetry reductions of Cauchy Problems for Fourth-Order Quasi-Linear Parabolic Equations

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Communications in Theoretical Physics 2010年第1期53卷 28-36页

作者：李吉娜张顺利苏敬蕊 Center for Nonlinear Studies Department of Mathematics Northwest University Center of Nonlinear Science Ningbo University

This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries （GCSs）. Complete group classificati... 详细信息

关键词： fourth-order quasi-linear parabolic equation symmetry reduction Cauchy problem

symmetry reductions of Two-Dimensional Variable Coefficient Burgers Equation

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Communications in Theoretical Physics 2005年第5期43卷 861-866页

作者： ZHANGXiao-Ling LIBiao DepartmentofAppliedMathematics DalianUniversityofTechnologyDalian116024China DepartmentofAppliedMathematics DalianUniversityofTechnologyDalian116024China／／KeyLaboratoryofMathematicsMechanizationtheChineseAcademyofSciencesBeijing100080China

By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial dif... 详细信息

关键词： variable coefficient Burgers equation symmetry reduction

symmetry reductions of a Lax Pair for(2+1)-Dimensional Differential Sawada-Kotera Equation

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Communications in Theoretical Physics 2009年第5期51卷 777-780页

作者： ZHI Hong-Yan School of Mathematics and Computational Sciences China University of Petroleum Dongying 257061 China

Based on the symbolic computational system Maple, the similarity reductions of a Lax pair for the （2＋1 ）-dimensional differential Sawada Kotera （SK） equation by the classical Lie point group method, are presented. We obtain several interesting reductions. Comparing the reduced Lax pair＇s compatibility with the reduced SK equation under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced SK equation. In general, the reduced equations are the subsets of the compatibility conditions of the reduced Lax pair.

关键词： classical Lie group approach symmetry reduction Lax pair Sawada-Kotera equation

symmetry reductions and Group-Invariant Solutions of (2+1)-Dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

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Communications in Theoretical Physics 2010年第4期53卷 591-595页

作者：吕娜梅建琴张鸿庆 School of Mathematical Sciences Dalian University of Technology

With the aid of symbolic computation, we present the symmetry transformations of the (2+1)-dimensionalCaudrey-Dodd Gibbon-Kotera-Sawada equation with Lou's direct method that is based on Lax pairs. Moreover, withthe symmetry transformations we obtain the Lie point symmetries of the CDGKS equation, and reduce the equation withthe obtained symmetries. As a result, three independent reductions are presented and some group-invariant solutions ofthe equation are given.

关键词： symmetry reduction Caudrey-Dodd-Gibbon-Kotera-Sawada equation Lou's direct method group-invariant solution