修正Boussinesq方程的N-次Darboux变换与精确解  

N-fold Darboux Transformation and Exact Solutions of the Modified Boussinesq Equation

作　　者：乌日乐 套格图桑[1,2] 扎其劳 Wurile;Taogetusang;Zhaqilao(College of Mathematical Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematics,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2023年第1期81-86,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11861050,11361040);内蒙古自治区自然科学基金资助项目(2020LH01010,2020LH01008);内蒙古师范大学基本科研业务费专项资助项目(2022JBZD011,2022JBTD007)。

摘　　要：基于一个3×3矩阵Lax对,研究修正Boussinesq方程的N-次Darboux变换。首先给出修正Boussinesq方程Darboux变换的简捷证明。其次通过迭代给出N-次Darboux变换,最后利用Darboux变换获得修正Boussinesq方程和Boussinesq方程的精确解。N-fold Darboux transformation of the modified Boussinesq equation is established and studied based on its Lax pair with3 × 3matrix in the paper. Firstly, a simple proof for the Darboux transformation of modified Boussinesq equation is given. Secondly, N-fold Darboux transformation is derived by iterations. And then, the exact solutions of the modified Boussinesq equation and Boussinesq equation are obtained.

关 键 词：BOUSSINESQ方程 DARBOUX变换 3×3矩阵Lax对 精确解 

分 类 号：O175.29[理学—数学]