Periodic finite-genus solutions of the KdV equation are orbitally stable

PHYSICA D-NONLINEAR PHENOMENA

卷:239

Article

Nivala, Michael¹  Deconinck, Bernard¹ 

[1] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA

关键词: Stability;    Korteweg-de Vries equation;    Periodic solutions;   

DOI  :  10.1016/j.physd.2010.03.005

来源: Elsevier

【 摘 要 】

The stability of periodic solutions of partial differential equations has been an area of increasing interest in the last decade. The KdV equation is known to have large families of periodic solutions that are parameterized by hyperelliptic Riemann surfaces. They are generalizations of the famous multi-soliton solutions. We show that all such periodic solutions are orbitally stable with respect to subharmonic perturbations: perturbations that are periodic with period equal to an integer multiple of the period of the underlying solution. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free