Existence and stability of solitary waves for the generalized Korteweg-de Vries equations

Boundary value problems

Mingli Hong¹ 

[1] Institute of Disaster Prevention, Sanhe Hebei, China

关键词: generalized Korteweg-de Vries equations;    constrained minimization problems;    concentration-compactness;    stability;   

DOI  :  10.1186/1687-2770-2013-121

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we consider the fractional Korteweg-de Vries equations with general nonlinearities. By studying constrained minimization problems and applying the method of concentration-compactness, we obtain the existence of solitary waves for the generalized Korteweg-de Vries equations under some assumptions of the nonlinear term. Moreover, we prove that the set of minimizers is a stable set for the initial value problem of the equations, in the sense that a solution which starts near the set will remain near it for all time.

【 授权许可】

CC BY