Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (4): 998-1018.doi: 10.1016/S0252-9602(17)30054-1

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ORBITAL STABILITY OF PERIODIC TRAVELING WAVE SOLUTIONS TO THE GENERALIZED ZAKHAROV EQUATIONS

Xiaoxiao ZHENG1, Yadong SHANG2, Xiaoming PENG2   

  1. 1. School of Mathematical Sciences, Qufu Normal University, Qufu 273155, China;
    2. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
  • Received:2016-04-14 Revised:2016-12-17 Online:2017-08-25 Published:2017-08-25
  • Contact: Xiaoxiao ZHENG,E-mail:xiaoxiaozheng87@163.com E-mail:xiaoxiaozheng87@163.com
  • About author:Yadong SHANG,E-mail:gzydshang@126.com;Xiaoming PENG,pengxm1987@163.com
  • Supported by:

    This work is supported by the National Natural Science Foundation of China (11401122) and Science and technology project of Qufu Normal University (xkj201607).

Abstract:

This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations
First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of[15, 16, 19].

Key words: generalized Zakharov equations, periodic traveling waves, orbital stability

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