Stability of solitary traveling waves of moderate amplitude with non-zero boundary

Boundary value problems

Shan Zheng¹  Zhengyong Ouyang² 

[1] Department of Basic Courses, Guangzhou Maritime Institute, Guangzhou, P.R. China;Department of Mathematics, Foshan University, Guangdong, P.R. China

关键词: moderate amplitude;    solitary traveling waves with non-zero boundary;    orbital stability;    35Q51;    35A35;    35B30;    35G25;   

DOI  :  10.1186/s13661-017-0809-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Considered here is the stability problem of solitary traveling waves with non-zero boundary of an equation describing the free surface waves of moderate amplitude in the shallow water regime. We employ a transform to convert the stability problem of solitary waves with non-zero boundary to the same one of solitary waves vanishing at infinity for a new equation, such that the abstract stability theorem proposed by Grillakis et al. can work on it. We then show that the solitary traveling waves with non-zero boundary are orbitally stable under certain parameter conditions.

【 授权许可】

CC BY