Transverse Spectral Stability of Small Periodic Traveling Waves for the KP Equation

DOI10.1111/j.1467-9590.2010.00501.xzbMath1218.35208arXiv1004.2183OpenAlexW1954557985MaRDI QIDQ3082631

Mariana Haragus

Publication date: 16 March 2011

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.2183

zbMATH Keywords

stabilitytraveling wavesKadomtsev-Petviashvili equation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Traveling wave solutions (35C07)

Related Items

Counting unstable eigenvalues in Hamiltonian spectral problems via commuting operators ⋮ Transverse dynamics of two-dimensional gravity-capillary periodic water waves ⋮ Stability of line solitons for the KP-II equation in ℝ² ⋮ Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations ⋮ Transverse Orbital Stability of Periodic Traveling Waves for Nonlinear Klein-Gordon Equations ⋮ Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation ⋮ Transverse spectral instabilities in Konopelchenko–Dubrovsky equation ⋮ Transverse dynamics of two-dimensional traveling periodic gravity-capillary water waves ⋮ The Phase Shift of Line Solitons for the KP-II Equation ⋮ Whitham modulation theory for the Kadomtsev– Petviashvili equation ⋮ A simple criterion for transverse linear instability of nonlinear waves ⋮ Modulational Instability in the Whitham Equation for Water Waves ⋮ Stability of traveling wave solutions of nonlinear dispersive equations of NLS type ⋮ On the Spectral and Orbital Stability of Spatially Periodic Stationary Solutions of Generalized Korteweg-de Vries Equations ⋮ Transverse instability of periodic and generalized solitary waves for a fifth-order KP model ⋮ Transverse linear stability of line periodic traveling waves for water-wave models

Uses Software

• SpectrUW

Cites Work

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• Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's
• Transverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev–Petviashvili Equation

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