修正cKdV方程组的孤立波结构及其稳定性

Solitary Wave Solutions of Modified Coupled KdV Equation and Their Stability

利用函数展开法求解修正耦合KdV(Coupled KdV,cKdV)方程组,得到几类孤立波解,包括扭结型—钟型、双扭结型、双钟型以及双扭结—双钟型结构的单孤子解.在不同的极限情况下,这些解分别退化为修正cKdV方程的扭结状或钟状孤波解.对孤立波的稳定性进行了数值研究,结果表明:修正cKdV方程既存在稳定的孤立波解,也存在不稳定的孤立波解.

With function expansion method,we obtain several types of solitary wave solutions of modified coupled KdV（cKdV） equations,including kink-bell-like soliton,double kinks soliton,double bells soliton and double kinks-double bells soliton.These solitary wave solutions are reduced to kink or bell-like solitons solution under different limitations.We also investigate numerically stability of solitary wave solutions.It indicates that the system of modified cKdV equations has both stable solitary wave solutions and unstable solitary wave solutions.