KdV方程的孤子-椭圆周期波解及其准孤立子行为

以KdV方程为例讨论了孤子-椭圆周期波解的准孤立子行为及其相互作用性质. 首先应用推广的tanh函数展开法构造了KdV方程的孤子-椭圆周期波解及其准孤立子极限, 并由孤子-椭圆周期波解的“穿衣服”结构给出了周期波的相移公式. 此外, 结合国内外研究前沿, 讨论了该解的物理应用.

Soliton-cnoidal wave solution and its quasi-soliton behavior to the Korteweg-de Vries equation

In this paper, a soliton-cnoidal wave solution with its quasi-soliton behavior to the Korteweg-de Vries equation is obtained using the generalized tanh expansion method. Firstly, the extended tanh function expansion method is used to construct the soliton-elliptic periodic wave solution of the KdV equation and its quasi-solitary limit. The phase shift formula of the periodic wave is given by the “clothing” structure of the soliton-elliptic periodic wave solution. In addition, combined with domestic and foreign research frontiers, the physical application of the solution is discussed.