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Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
Hur, Vera Mikyoung Johnson, Mathew A.
Hur, Vera Mikyoung
Johnson, Mathew A.
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Abstract
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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Date
2015-09-17
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Society for Industrial and Applied Mathematics
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Keywords
Stability, Periodic traveling waves, nonlinear dispersive, nonlocal
Citation
Hur, V. M., & Johnson, M. A. (2015). Stability of periodic traveling waves for nonlinear dispersive equations. SIAM Journal on Mathematical Analysis, 47(5), 3528-3554.