广义变系数Kadomtsev-Petviashvili方程的孤子解

Soliton Solution for the General Variable-Coefficient Kadomtsev-Petviashvili Equation

借助多元变换技巧,将广义变系数Kadomtsev-Petviashvili方程约化为常系数(2+1)维Kadomtsev-Petviashvili方程,基于Hirota双线性方法,按照Wronskian技巧,可以得到常系数Kadomtsev-Petviashvili方程的精确解,再运用多元变换,构造出广义变系数Kadomtsev-Petviashvili方程一般化的单孤子解、双孤子解以及N孤子解,并且展示出单、双孤子解的非线性动力学过程,这将有助于理解孤波的演化发展.

With the help of the multivariate transformation technique,the general variablecoefficient Kadomtsev-Petviashvili equation is reduced to constant-coefficient(2+1)dimensional Kadomtsev-Petviashvili equation,based on the Hirota bilinear method,the exact solutions of constant-coefficient Kadomtsev-Petviashvili equation were obtained according to Wronskian technique,then using the multivariate transformation,the generalised one-soliton solutions、two-soliton solutions and N-soliton solutions of the general variable-coefficient Kadomtsev Petviashvili equation are presented,and the nolinear dynamics process of the one-and two-soliton solutions are showed which can help us better understand the evolution of soliton waves.