一类变系数Boussinesq型方程的Darboux变换及多孤子解  

Darboux Transformation and Soliton Solutions for the Variable-coefficient Variant Boussinesq-like Equation

作　　者：杨苗苗[1] 王涛[2] 李雪梅 YANG Miao-miao;WANG Tao;LI Xue-mei(Department of Public Basic Courses Teaching, Zhengzhou Institute of Technology, Zhengzhou 450000 China;Base Depart, Zhengzhou University of Science Technology, Zhengzhou 450000, China;School of Mathematics and Statistics, Zhengzhou University Zhengzhou 450000, China)

机构地区：[1]郑州理工职业学院公共基础教学部,河南郑州450000 [2]郑州科技学院基础部,河南郑州450000 [3]郑州大学数学与统计学院,河南郑州450000

出　　处：《数学的实践与认识》2018年第8期206-211,共6页Mathematics in Practice and Theory

基　　金：河南省教育厅重点科研项目(16A480012);国家自然科学基金(11171312)

摘　　要：主要讨论在某种约束下,变系数Boussinesq型方程和变系数Broer-KaupKupershmidt方程之间的联系,构造变系数Broer-Kaup-Kupershmidt方程的另外一种Darboux变换,且应用Darboux变换得到变系数Boussinesq型方程的孤子解.In this paper,connection between the variable-coefficient variant Boussinesq-like equation and a variable-coefficient Broer-Kaup-Kupershmidt equation is revealed under certain constraints. Based on the resulting Lax pairs, a new Darboux transformation with multi-parameters for the variable-coefficient Broer-Kaup-Kupershmidt equation is constructed with the help of a gauge transformation. As an application, soliton solutions of the variable- coefficient variant Boussinesq-like equations are given.

关 键 词：变系数Boussinesq型方程 变系数Broer-Kaup-Kupershmidt方程 DARBOUX变换 孤子解 

分 类 号：O175[理学—数学]