具有扩散项的广义Nizhnik-Novikov-Veselov方程孤立波与周期波  

Solitary wave and periodic wave for a generalized Nizhnik-Novikov-Veselov equation with diffusion term

作　　者：杜增吉 林晓洁 余姗姗 Zengji Du;Xiaojie Lin;Shanshan Yu

机构地区：[1]江苏师范大学数学与统计学院,徐州221116

出　　处：《中国科学：数学》2022年第2期133-154,共22页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11871251和11771185)资助项目。

摘　　要：本文研究具有弱向后扩散项的广义Nizhnik-Novikov-Veselov方程;通过运用动力系统方法,特别是几何奇异摄动理论和不变流形理论,得到方程孤立波解与周期波解的存在性;通过计算Abel积分的比值得到波速的单调性.同时给出了方程极限波速的上下界和周期波解的一些性质.This paper is concerned with a generalized Nizhnik-Novikov-Veselov equation with weak backward diffusion term.The existence of solitary wave and periodic wave solutions are obtained by using the method of the dynamical system,especially the geometric singular perturbation theory and invariant manifold theory.Furthermore,based on the ratio of the Abelian integral,the monotonicity of the wave speed is established.At the same time,the bounds of the limit wave speed and the properties of the periodic wave solutions to this equation are also given.

关 键 词：广义Nizhnik-Novikov-Veselov方程 孤立波 周期波 几何奇异摄动 ABEL积分 

分 类 号：O175[理学—数学]