On periodic waves for sine- and sinh-Gordon equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:379

Article

Natali, Fabio

关键词: Periodic waves;    Orbital instability;    Sine-Gordon equation;    Sinh-Gordon equation;   

DOI  :  10.1016/j.jmaa.2011.01.020

来源: Elsevier

【 摘 要 】

Results of existence as well as orbital stability/instability of periodic waves associated with sine-Gordon and sinh-Gordon equations will be treated in this manuscript. The sine-Gordon equation is known to be completely integrable, exactly solvable and it has several special solutions as soliton and breather solutions. We obtain in both cases, a periodic sign-changed wave which is smooth when posed on whole real line. The main tool used is the Grillakis, Shatah and Strauss' theory. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free