期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 47, 期 5, 页码 3528-3554出版社
SIAM PUBLICATIONS
DOI: 10.1137/12090215X
关键词
stability; periodic traveling waves; nonlinear dispersive; nonlocal
资金
- National Science Foundation [DMS-1008885, DMS-1211183]
- CAREER [DMS-1352597]
- University of Illinois at Urbana-Champaign [RB11162]
- University of Kansas General Research Fund [2302278]
We study the stability and instability of periodic traveling waves for Korteweg-de Vries-type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer for a suitable variational problem is nonlinearly stable to period preserving perturbations, provided that the associated linearized operator enjoys a Jordan block structure. We then discuss when the linearized equation admits solutions exponentially growing in time.
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