On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Daros, Alisson¹  Arruda, Lynnyngs Kelly² 

[1] Fed Univ Pampa, Dept Math, BR-97650000 Itaqui, Brazil

[2] Univ Fed Sao Carlos, Dept Math, PO B 676, BR-13565905 Sao Carlos, SP, Brazil

关键词: Traveling waves;    Instability;    Modified Camassa-Holm equation;   

DOI  :  10.1016/j.jde.2018.08.017

来源: Elsevier

【 摘 要 】

This paper is concerned with the orbital instability for a specific class of periodic traveling wave solutions with the mean zero property and large spatial period related to the modified Camassa-Holm equation. These solutions, called snoidal waves, are written in terms of the Jacobi elliptic functions. To prove our result we use the abstract method of Grillakis, Shatah and Strauss [23], the Floquet theory for periodic eigenvalue problems and the n-gaps potentials theory of Dubrovin, Matveev and Novikov [19]. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free