Nonlinear stability of Gardner breathers

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Alejo, Miguel A.¹ 

[1] Univ Fed Santa Catarina, Dept Matemat, Florianopolis, SC, Brazil

关键词: Gardner equation;    Modified KdV equation;    Breather;    Stability;   

DOI  :  10.1016/j.jde.2017.09.035

来源: Elsevier

【 摘 要 】

We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are H-2(R) stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov functional and we study the associated spectral problem, through (i) the analysis of the spectrum of explicit linear systems (spectral stability), and (ii) controlling degenerated directions by using low regularity conservation laws. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free