Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Haragus, Mariana^1,2  Wahlen, Erik³ 

[1] Univ Bourgogne Franche Comte, Inst FEMTO ST, F-25030 Besancon, France

[2] Univ Bourgogne Franche Comte, LMB, F-25030 Besancon, France

[3] Lund Univ, Ctr Math Sci, POB 118, S-22100 Lund, Sweden

关键词: Transverse stability;    Periodic waves;    Generalized solitary waves;    Dispersive equations;   

DOI  :  10.1016/j.jde.2016.11.025

来源: Elsevier

【 摘 要 】

We consider a fifth-order Kadomtsev Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free