(3+1)维广义非线性发展方程的双线性Backlund变换与精确解

Bilinear Bäcklund Transform and Exact Solutions to a(3+1)-Dimensional Generalized Nonlinear Evolution Equation

基于Hirota双线性方法和试探函数法,研究一个(3+1)维广义非线性发展方程的双线性Backlund变换和精确解问题。用Hirota双线性法,构造(3+1)维广义非线性发展方程的双线性形式和双线性Backlund变换。基于双线性形式和双线性Backlund变换,利用试探函数法与符号计算系统Mathematica,获得(3+1)维广义非线性发展方程的多种精确解,包括呼吸波解、复合型解、Lump周期解和孤子解,并分析解的相互作用情况。

The bilinear Bäcklund transformation and the exact solutions of a(3+1)dimensional generalized nonlinear development equation are studied based on the Hirota bilinear method and the trial function method in the paper.Firstly,the bilinear form and bilinear Bäcklund transformation of(3+1)⁃dimensional generalized nonlinear evolution equation are constructed by using Hirota bilinear method.Secondly,various exact solutions of(3+1)⁃dimensional generalized nonlinear evolution equation,including N⁃soliton solution,breather wave solution,compound solution,Lump periodic solution,Lump kink solution and soliton solution,are obtained by using trial function method and symbolic calculation system Mathematica based on bilinear form and bilinear Bäcklund transformation,and the interaction of the solutions is analyzed.