Generalized Zakharov-Kuzentsov方程的类孤子新解

J4 ›› 2015, Vol. 32 ›› Issue (3): 290-300.

Generalized Zakharov-Kuzentsov方程的类孤子新解

套格图桑, 伊丽娜

内蒙古师范大学数学科学学院，内蒙古呼和浩特 010022

收稿日期:2014-05-19 修回日期:2014-06-08 出版日期:2015-05-28 发布日期:2015-05-28

new soliton-like solution of the Generalized Zakharov-Kuzentsov equation

Taogetusang, Yi LiNa

College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022

Received:2014-05-19 Revised:2014-06-08 Published:2015-05-28 Online:2015-05-28

摘要/Abstract

摘要：

通过两个步骤,构造了Generalized Zakharov-Kuzentsov方程的无穷序列类孤子新解. 第一步、利用首次积分与函数变换,把一种非线性常微分方程转化为几种常用的辅助方程,并获得了几种常用辅助方程的新解、B\"{a}cklund变换和解的非线性叠加公式. 第二步、借助一系列的变换与符号计算系统~Mathematica,构造了Generalized Zakharov-Kuzentsov方程的无穷序列类孤子新解.

关键词: 辅助方程首次积分类孤子新解

Abstract:

By two steps, the paper structures the new infinite sequence soliton-like solution of the Generalized Zakharov-Kuzentsov equation. First, using the trick of the first integral and functional transformation, a kind of nonlinear ordinary differential equation is changed to some kinds of common auxiliary equations, and the new solutions of some common auxiliary equations, the Bäcklund transformation and the nonlinear superposition formula of solutions are obtained. Second, with the help of a sequence of transformations and the symbolic computation system Mathematic, the paper structures the new infinite sequence soliton-like solution of the Generalized Zakharov-Kuzentsov equation.

Key words: auxiliary equations first integral new soliton-like solution

套格图桑伊丽娜. Generalized Zakharov-Kuzentsov方程的类孤子新解[J]. J4, 2015, 32(3): 290-300.

Taogetusang, Yi LiNa. new soliton-like solution of the Generalized Zakharov-Kuzentsov equation[J]. J4, 2015, 32(3): 290-300.

参考文献

[1] Zheng Xuedong, Chen Yong, Li Biao, Zhang Hongqing. A new Generalization of extended tanh-function method for solving nonlinear evolution equations[J]. Commun.Theor.Phys.(Beijing),2003, 39: 647-652. [2] Taogetusang, Sirendaoerji. New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov-Kuzentsov equation[J]. Chin.Phys.,2006, 15(6):1143-1148. [3] Fu Zuntao, Chen Zhe, Liu Shikuo, Liu Shida. New solutions to Generalized mKdV equation[J]. Commun.Theor.Phys. (Beijing),2004, 41:25-28. [4] Mo Jiaqi, Zhang Weijiang, Chen Xianfeng. The homotopic solving method of solitary wave for strong nonlinear evolution equation[J]. Acta.Phys.Sin.(物理学报),2007, 56: 6169-6172(in Chinese). [5] Chen Yong, Li Biao, Zhang Hongqing. Bäcklund transformation and exact solutions for a new Generalized Zakharov-Kuzentsov equation with nonlinear terms of any order[J]. Commun.Theor.Phys.(Beijing),2003, 39: 135-140. [6] Chen Yong, Li Biao. New exact travelling wave solutions for Generalized Zakharov-Kuzentsov equations using general Projective Riccati equation method[J]. Commun.Theor.Phys.(Beijing),2004, 41:1-6. [7] Taogetusang, Sirendaoerji. New solitary wave solutions of the combined KdV equation with the variable coefficients[J].Chinese Journal of quantum electronics(量子电子学报),2009, 26(2):148-154(in Chinese). [8] Sirendaoreji, Sun Jiong. Auxiliary equation method for solving nonlinear partial differential equations [J]. Phys.Lett.,2003,A309:387-396. [9] Tian Guichen, Liu Xiqiang. Exact solutions of the general variable coefficient KdV equation with external term [J].Chinese Journal of quantum electronics(量子电子学报),2005, 22(3):339-343(in Chinese). [10] Taogetusang, Sirendaoerji. Jacobi elliptic function exact solutions of sine-Gordon equation[J].Chinese Journal of quantum electronics(量子电子学报),2009, 26(3):278-287(in Chinese). [11] Wang Mingliang, LI Lingxiao, LI Erqiang. Exact Solitary Wave Solutions of Nonlinear Evolution Equations with a Positive Fractional Power Term[J]. Commun.Theor.Phys. (Beijing),2014, 61: 7–14. [12] Chen Weilu, ZHANG Wenting, ZHANG Lipu, DAI Chaoqing. Interaction Behaviors Between Special Dromions in the (2+1)-Dimensional Broer–Kaup–Kupershmidt Equation[J]. Chin.Phys.,2013, 59: 68–72. [13] Ma Songhua, Fang Jianping. Peaked soliton solutions and interaction between solitons for the extended (2+1)-dimensional shallow water wave equation[J]. Acta.Phys.Sin.(物理学报),2012,61 180505(1-6)(in Chinese). [14] Ma Zhengyi, Ma Songhua, Yang Yi. Rational solutions and spatial solitons for the (2+1)-dimensional nonlinear schödinger equation with distributed coefficents[J].Acta.Phys.Sin.(物理学报), 2012,61 190508(1-5)(in Chinese). [15] Taogetusang, Sirendaoerji, Li Shumin. Infinite sequence soliton-like exact solutions of (2+1)-dimensional Breaking soliton equation[J]. Commun.Theor.Phys.(Beijing), 2011, 55(6): 949-954. [16] Zhang Jiefang, Guo Guanping, Wu Fengmin. New multi-soliton solutions and traveelling wave solutions of the dispersive long-wave equations[J]. Chin.Phys.,2002 ,11(6): 533-535. [17] Wang Junmin.Riemann θ function solutions to modified Korteweg de Vries-sine-Gordon equation [J]. Acta.Phys.Sin.(物理学报),2012, 61(8): 080201(1-5)(in Chinese). [18] Taogetusang, Narenmandula. New infinite sequence exact solutions of nonlinear evolution equations with variable coefficients by the second kind of elliptic equation[J].Acta.Phys.Sin.(物理学报), 2011,60 090201(1-12)(in Chinese).