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Doubly Periodic Propagating Wave for (2+1)-Dimensional breaking soliton equation

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Communications in Theoretical Physics 2008年第2期49卷 268-274页

作者： HUANG Wen-Hua LIU Yu-Lu ZHANG Jie-Fang College of Science Huzhou University Huzhou 313000 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China Institute of Nonlinear Physics Zhejiang Normal University Jinhua 321000 China

Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋1）-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic.

关键词： breaking soliton equation variable separation method Jabobi elliptic function periodic wave

Reduction and New Explicit Solutions of （2＋1）-Dimensional breaking soliton equation

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Communications in Theoretical Physics 2006年第1期45卷 33-35页

作者： TIAN Ying-Hui CHEN Han-Lin LIU Xi-Qiang School of Mathematics and Physics Southwest University of Science and Technology Mianyang 621010 China School of Mathematics Sciences Liaocheng University Liaocheng 252059 China

Abstract By applying the Lie group method, the （2＋l）-dimensional soliton equation is reduced to some （1＋1）-dimensional nonlinear equations. Based upon some new explicit solutions of the （2＋1）-dimensional brea... 详细信息

关键词： breaking soliton equation Lie group method symmetry explicit solution

A Note on "Doubly Periodic Propagating Wave for (2+1)-Dimensional breaking soliton equation"

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Communications in Theoretical Physics 2009年第1期51卷 79-80页

作者： ZHENG Chun-Long PAN Zhen-Huan MA Zheng-Yi School of Physics and Mechanical Engineering Shaoguan University Shaoguan 512005 China College of Mathematics and Physics Lishui University Lishui Zhejiang 323000 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

In a recent paper [Commun. Theor. Phys. （Beijing, China） 49 （2008） 268], Huang et al. gave a general variable separation solution to the （2＋1）-dimensional breaking soliton equation via a special Biicldund transformation and the variable separation approach. In terms of the derived variable separation solution and by introducing Jacobi elliptic functions, they claimed that nonelastic types of interaction between Jacobi elliptic function waves are investigated both analytically and graphically. We show that some inappropriateness or errors exist in their paper, and say nothing of the conclusion that some nonelastic types of interaction between Jacobi elliptic function waves in the （2＋1）-dimensional breaking soliton equation have been found.

关键词： breaking soliton equation variable separation solution interaction comment

Symmetries and Exact Solutions of the breaking soliton equation

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Communications in Theoretical Physics 2011年第11期56卷 851-855页

作者：陈美刘希强 School of Mathematical Sciences Liaocheng University

With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)*** symmetries,we find six classical similarity reductions and two nonclassical similarity reductions of the BS *** of exact solutions of the BS equation are obtained by solving the reduced equations.

关键词： breaking soliton equation symmetry similarity reductions exact solutions

Stable-range Approach to the （2＋1）-dimensional breaking soliton and Kadomtsev-Petviashvili equations

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Chinese Quarterly Journal of Mathematics 2012年第2期27卷 183-190页

作者： ZHANG Ying LI Ji-na ZHA NG Jiang-hong SONG Xiao-qian Department of Mathematics Northwest University Xi'an 710069 China College of Science Zhongyuan University of Technology Zhengzhou 450007 China Department of Physical Education Tianshui Normal University Tianshui 741001 China School of Mathematics and Statistics Chongqing Three Gorges University Chongqing 404199 China

By using Xu's stable-range method,families of explicit exact solutions with multiple parameter functions for the(2+1)-dimensional breaking soliton and KadomtsevPetviashvili *** parameter functions make our solutions m... 详细信息

关键词： exact solutions breaking soliton equation Kadomtsev-Petviashvili equation Stable-range