广义耦合KdV孤子方程的达布变换及其偶孤子解  

Darboux Transformation of Generalized Coupled KdV Soliton Equation and its Even-soliton Solutions

作　　者：刘萍[1] 

机构地区：[1]西南大学数学与统计学院应用数学系,四川重庆400715

出　　处：《数学物理学报（A辑）》2009年第5期1213-1222,共10页Acta Mathematica Scientia

基　　金：西南大学学校青年基金(SWUQ2006028)资助

摘　　要：根据广义耦合KdV孤子方程的Lax对,借助谱问题的规范变换,一个包含多参数的达布变换被构造出来.利用达布变换来产生广义耦合KdV孤子方程的偶孤子解,并且用行列式的形式来表达广义耦合KdV孤子方程的偶孤子解.作为应用,广义耦合KdV孤子方程的偶孤子解的前两个例子被给出.Based on the resulting Lax pairs of the generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem.By using the Darboux transformation,the generalized even-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form.As an application,the first two cases are given.

关 键 词：达布变换 孤子方程 偶孤子解 规范变换 

分 类 号：O175.29[理学—数学]