(2+1)维耦合KdV方程达布变换间的关系及其孤子解  

Relation among Darboux transformations for (2+1) dimensional coupled KdV equation and its soliton solution

作　　者：黄坤[1] 陈友军[1] 

机构地区：[1]华北水利水电学院数学与信息科学学院,郑州450011

出　　处：《黑龙江大学自然科学学报》2013年第1期71-78,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10901142)

摘　　要：从KdV方程的谱问题出发,推导出它的孤子方程族,并由前两个非平凡的孤子方程导出一个新的(2+1)维耦合KdV方程及其对应的Lax对。借助零曲率方程得到三种达布变换,并讨论三种达布变换间的关系。借助达布变换,解出(2+1)维耦合KdV方程的孤子解及研究解的性态。利用计算机数学软件,画出了孤子解各种碰撞图形。Hierarchy of soliton equations of KdV equation is obtained from its spectral problem. Based on the first two nontrivial soliton equations, a new （ 2 ＋ 1 ） dimensional coupled KdV equation and its Lax pair are derived. With the help of zero curvature equation, three Darboux transformations （DTs） are obtained, and further relations among these three DTs are discussed. By an application of DT, the multiple soliton solutions of （2 ＋ 1 ） dimensional coupled KdV equation are given, and properties of solutions are discussed. Using mathematical software, various collision graphics of the soliton solutions are given.

关 键 词：KDV方程 达布变换 孤子解 

分 类 号：O175.29[理学—数学]