修正KdV-sinh-Gordon方程的实N孤子解及复N孤子解

The real N soliton solutions and complex N soliton solutions of modified KdV-sinh-Gordon equation

研究了修正KdV-sinh-Gordon(mKdV-SHG)方程的孤子解及孤子分子的存在条件。首先借助Hirota双线性导数法对mKdV-SHG方程进行双线性化,利用双线性形式求出该方程的单孤子解、双孤子解、三孤子解并画出其三维图形,然后在此基础上计算出实N孤子解和复N孤子解,最后验证了孤子分子的存在,并得出其存在条件。

In this paper,the soliton solutions of the modified KdV-sinh-Gordon(mKdV-SHG)equation and the existence conditions of the soliton molecules are studied.Firstly,the mKdV-SHG equation is bilinear with the aid of the Hirota bilinear derivative method.The single soliton solution,two-soliton solutions and three-soliton solutions of the equation are obtained by using the bilinear form,and their three-dimensional graphs are drawn.On this basis,the real N soliton solution and complex N soliton solution are calculated.Finally,the existence of the soliton molecules are verified and the conditions for its existence are obtained.