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

作　　者：郭博文 康景峰 GUO Bowen;KANG Jingfeng(College of Science,Zhongyuan University of Technology,Zhengzhou 451191,China)

机构地区：[1]中原工学院理学院,河南郑州451191

出　　处：《河南工程学院学报（自然科学版）》2022年第1期70-75,共6页Journal of Henan University of Engineering：Natural Science Edition

基　　金：国家自然科学基金(11705290);河南省科技攻关计划(202102210363)。

摘　　要：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.

关 键 词：修正KdV-sinh-Gordon方程 Hirota双线性导数法 孤子分子 N孤子解 

分 类 号：O175[理学—数学]