形变Boussinesq型方程族及其守恒律和Darboux变换  

A Deformed Boussinesq-Type Hierarchy, Conservation Laws and Darboux Transformation

作　　者：何国亮 郑真真 徐涛 He Guoliang;Zheng Zhenzhen;Xu Tao(School of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou 450002)

机构地区：[1]郑州轻工业大学数学与信息科学学院,郑州450002

出　　处：《数学物理学报（A辑）》2020年第5期1305-1318,共14页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871232);河南省高等学校青年骨干教师培养计划基金

摘　　要：该文借助于零曲率方程得到了一个与3×3矩阵谱问题相关的形变Boussinesq型非线性演化可积方程族.通过考虑两个线性谱问题,给出了方程族中前两个方程的无穷多守恒律.借助于Darboux变换得到了第一个形变Boussinesq型方程的一些显式解.In this paper,we propose a deformed Boussinesq-type integrable hierarchy of nonlinear evolution equations associated with a 3×3 matrix spectral problem by using the zero-curvature equation.Based on two linear spectral problems,we obtain the infinite many conservation laws of the first two members in the hierarchy.Some explicit solutions to the first deformed Boussinesq-type equation are given by utilizing the Darboux transformation.

关 键 词：形变Boussinesq型方程族 守恒律 DARBOUX变换 

分 类 号：O175[理学—数学]