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new exact solutions for a Class of Nonlinear Coupled Differential Equations

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Communications in Theoretical Physics 2005年第5期43卷 781-786页

作者： ZHAOHong GUOJun BAICheng-Lin HANJi-Guang PhysicalScienceandInformationEngineeringSchool LiaochengUniversityLiaocheng252059China AdultEducationCollege ShandongEconomicsUniversityJinan250014China

More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance m... 详细信息

关键词： nonlinear couple differential equations new exact solutions hyperbola function transform method

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

Symmetry Groups and new exact solutions to （2＋1）-Dimensional Variable Coefficient Canonical Generalized KP Equation

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Communications in Theoretical Physics 2007年第3X期48卷 405-410页

作者： ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin Department of Mathematics Dezhou College Dezhou 253023 China 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 modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.

关键词： (2+1)-dimensional variable coefficient canonical generalized KP (VCCGKP) equation modified CK's'direct method symmetry groups Lie symmetry similarity reductions new exact solutions