(2+1)维耦合KdV方程达布变换间的关系及其孤子解

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.