形变Boussinesq型方程族及其守恒律和Darboux变换

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1305-1318.

形变Boussinesq型方程族及其守恒律和Darboux变换

何国亮*(),郑真真,徐涛

^{郑州轻工业大学数学与信息科学学院郑州 450002}

收稿日期:2018-11-13 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 何国亮 E-mail:glhemath@163.com
基金资助:
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

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

Guoliang He*(),Zhenzhen Zheng,Tao Xu

^{School of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002}

Received:2018-11-13 Online:2020-10-26 Published:2020-11-04
Contact: Guoliang He E-mail:glhemath@163.com
Supported by:
the NSFC(11871232);the Training Plan of Young Key Teachers in Universities of Henan Province

摘要/Abstract

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.

关键词: 形变Boussinesq型方程族, 守恒律, Darboux变换

Abstract:

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.

Key words: Deformed Boussinesq-type hierarchy, Conservation laws, Darboux transformation

中图分类号:

O175

何国亮,郑真真,徐涛. 形变Boussinesq型方程族及其守恒律和Darboux变换[J]. 数学物理学报, 2020, 40(5): 1305-1318.

Guoliang He,Zhenzhen Zheng,Tao Xu. A Deformed Boussinesq-Type Hierarchy, Conservation Laws and Darboux Transformation[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1305-1318.

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