修正的Korteweg de-Vries方程的孤立波和周期波相互作用解

摘要

修正的Korteweg de Vries方程有许多形式的解，例如孤立波解、周期波解等，是一个十分重要的物理模型。利用截断的Painlevé分析和tanh函数展开法，成功解决了修正的Korteweg de Vries方程的孤立波与其他形式波的相互作用形式。尤其是通过雅克比椭圆积分和第三类的不完全积分得到了修正的Korteweg de Vries方程的椭圆正弦波解。%The modified Korteweg de Vries equation which is considered as an important model in nonlinear physics has various forms of solutions,such as solitary wave solution,periodic wave solution and so on.Using the truncated Painlevéanalysis and the generalized tanh function expansion approach,the interaction solution among soliton and other types of nonlinear excitations of the modified Korteweg de Vries (mKdV)equation can be obtained,particularly,the soliton cnoidal wave interaction solutions are studied by means of the Jacobi elliptic functions and the third type of incomplete elliptic integrals.