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Exact Solutions to (2+1)-Dimensional Kaup-Kupershmidt Equation

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Communications in Theoretical Physics 2009年第11期52卷 795-800页

作者： LU Hai-Lin liu xi-qiang School of Mathematical Sciences Liaocheng University Liaocheng 252059 China

In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the （2＋1）-dimensional Kaup-Kupershmidt （KK） equation are presented. We successfully obtain more general exact travelling wave solutions for （2＋ 1）-dimensional KK equation by the symmetry method and the （G1/G）-expansion method. Consequently, we find some new solutions of （2＋1）-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions.

关键词： (2+1)-dimensional Kaup-Kupershmidt equation the symmetry method the (G1/G)-expansion method exact solutions

Explicit Solutions of (2+1)-Dimensional Canonical Generalized KP, KdV, and (2+1)-Dimensional Burgers Equations with Variable Coefficients

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Communications in Theoretical Physics 2009年第11期52卷 784-790页

作者： ZHANG Lin-Lin liu xi-qiang School of Mathematical Sciences Liaocheng University Liaocheng 252059 China

In this paper, using the generalized （G1/G）-expansion method and the auxiliary differential equation method, we discuss the （2＋1）-dimensional canonical generalized KP （CGKP）, KdV, and （2＋1）-dimensional Burgers equations with variable coetticients. Many exact solutions of the equations are obtained in terms of elliptic functions, hyperbolic functions, trigonometric functions, and rational functions.

关键词： generalized (G1/G)-expansion method auxiliary equation exact solution

New Exact Solutions and Conservation Laws to （3＋1）-Dimensional Potential-YTSF Equation

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Communications in Theoretical Physics 2006年第3期45卷 487-492页

作者： ZHANG Li-Hua liu xi-qiang School of Mathematical Science Liaocheng University Liaocheng 252059 China

Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK＇s direct method, we build the relationship between new solutions and old ones and the （3＋1）-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the （3＋1）-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry.

关键词： new exact solutions Lie point symmetry groups conservation laws (3+1)-dimensional potential-YTSF equation

Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations

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Communications in Theoretical Physics 2005年第3X期44卷 479-482页

作者： YAN Zhi-Lian liu xi-qiang School of Mathematical Sciences Liaocheng University Liaocheng 252059 China

By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.

关键词： approximate equations for long water waves variant Boussinesq equations non-traveling wave solution solitary wave solution

Symmetry Reductions and Explicit Solutions for a Generalized Zakharov-Kuznetsov Equation

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Communications in Theoretical Physics 2006年第1期45卷 29-32页

作者： YAN Zhi-Lian liu xi-qiang School of Mathematical Sciences Liaocheng University Liaocheng 252059 China

Two types of symmetry of a generalized Zakharov-Kuznetsov equation are obtained via a direct symmetry method. By selecting suitable parameters occurring in the symmetries, we also find some symmetry reductions and new... 详细信息

关键词： generalized Zakharov-Kuznetsov equation symmetry explicit solution

Study of （2＋1）-Dimensional Higher-Order Broer-Kaup System

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Communications in Theoretical Physics 2007年第3期47卷 403-408页

作者： WANG Ling liu xi-qiang DONG Zhong-Zhou School of Mathematical Sciences Liaocheng University Liaocheng 252059 China Department of Mathematics Chizhou Teacher＇s College Chizhou 247000 China

Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry *** to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.

关键词： (2+1)-dimensional HBK system Painleve property symmetries exact solution conservation laws

Symmetry Reductions, Exact Solutions and Conservation Laws of Asymmetric Nizhnik-Novikov-Veselov Equation

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Communications in Theoretical Physics 2008年第1期49卷 1-8页

作者： WANG Ling DONG Zhong-Zhou liu xi-qiang Department of Mathematics and Computer Science Chizhou University Chizhou 247000 China Software Engineering Institute East China Normal University Shanghai 200062 China School of Mathematics Sciences Liaocheng University Liaocheng 252059 China

By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation （ANNV）. Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.

关键词： direct symmetry method ANNV equation optimal system explicit solution conservation laws

Symmetry, Reductions and New Exact Solutions of ANNV Equation Through Lax Pair

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Communications in Theoretical Physics 2008年第7期50卷 1-6页

作者： ZHANG Li-Hua liu xi-qiang BAI Cheng-Lin Department of Mathematics Dezhou University Dezhou 253023 China School of Mathematical Sciences Liaocheng University Liaocheng 252059 China School of Physical Science and Information Engineering Liaocheng University Liaocheng 252059 China

In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.

关键词： ANNV equation direct symmetry method Lax pair reductions new exact solutions

New Multiple Soliton-like and Periodic Solutions for （2＋l）-Dimensional Canonical Generalized KP Equation with Variable Coefficients

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Communications in Theoretical Physics 2006年第5X期46卷 793-798页

作者： ZHANG Li-Hua liu xi-qiang BAI Cheng-Lin School of Mathematical Sciences Liaocheng University Liaocheng 252059 China School of Physics Science and Information Engineering Liaocheng University Liaocheng 252059 China

In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the （2＋1）-dimensional OGKP equation with variable coetffcients.

关键词： (2+1)-dimensional canonical generalized (CGKP) equation with variable coefficients tanh function method Riccati equation soliton-like and periodic solutions