色散长波方程的Darboux变换及多孤子解

根据色散长波方程的可积性,首先借助符号计算构造出该方程的Lax对,接着构建一个包含多参数的Darboux变换,通过应用Darboux变换,得到色散长波方程的2N-孤子解,最后通过图像研究了孤子解的性质,这些解和图像可能对解释色散长波方程所描述的水波现象有所帮助.

Darboux Transformation and Multi-Soliton Solutions of The Dispersive Long-Wave Equations

In this paper,firstly,with the aid of symbolic computation Maple,the Lax pair for the dispersive long-wave equations is explicitly constructed by use of its Painleve property. Secondly,based on the resulting Lax pairs.the Darboux transformation with multi-parameters for that system is presented.By applying the Darboux transformation,we obtain new explicit (2N)-soliton solutions of that system.Finally,the properties for these solutions are graphically studied,which might be helpful to understand water wave propagation processes discirbed by that system.