一个非线性演化方程的达布变换  

Darboux transformation of a nonlinear evolution equation

作　　者：朱赛柯 李芳[1] Zhu Saike;Li Fang(College of Science,Henan University of Technology,Zhengzhou 450001,China)

机构地区：[1]河南工业大学理学院,河南郑州450001

出　　处：《纯粹数学与应用数学》2022年第2期214-223,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(11601123)。

摘　　要：主要研究一个与三阶谱问题相联系的非线性演化方程的Darboux变换及其精确解.首先从空间部分谱问题出发,找到其辅谱问题,然后基于该方程的Lax对构造出该方程所满足的Darboux变换,并确定新旧位势之间的关系,最后选取合适的种子解,利用Darboux变换得到方程的精确解的表达式.In this paper, the Darboux transformation and exact solution of a nonlinear evolution equation related to the third-order spectral problem is studied. The temporal partial spectral problem is found from the spatial partial spectral problem. With the help of the Lax pairs of the equation,the Darboux transformation for the equation is constructed, and the relationship between the new and old potential is proved. Finally, the exact solution of the equation is obtained by using the Darboux transformation and selecting the appropriate seed solutions.

关 键 词：谱问题 非线性演化方程 达布变换 精确解 

分 类 号：O175[理学—数学]