Enter stable manifolds around line solitary waves of the zakharov-kuznetsov equation with critical speed

研究成果: Contribution to journalArticle査読

抄録

In this paper, we construct center stable manifolds around unstable line solitary waves of the Zakharov{Kuznetsov equation on two dimensional cylindrical spaces R TL (TL = R=2 LZ). In the paper [39], center stable manifolds around unstable line solitary waves have been constructed excluding the case of critical speeds c 2 f4n2=5L2; n 2 Z; n > 1g. In the case of critical speeds c, any neighborhood of the line solitary wave with speed c in the energy space includes solitary waves which are depend on the direction TL. To construct center stable manifolds including their solitary waves and to recover the degeneracy of the linearized operator around line solitary waves with critical speed, we prove the stability condition of the center stable manifold for critical speed by applying to the estimate of the 4th order term of a Lyapunov function in [37] and [38].

本文言語英語
ページ(範囲)3579-3614
ページ数36
ジャーナルDiscrete and Continuous Dynamical Systems- Series A
41
8
DOI
出版ステータス出版済み - 8 2021
外部発表はい

All Science Journal Classification (ASJC) codes

  • 分析
  • 離散数学と組合せ数学
  • 応用数学

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