Transverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev–Petviashvili Equation
From MaRDI portal
Publication:5198429
DOI10.1137/090770758zbMath1233.35025arXiv0909.1857OpenAlexW2153750318MaRDI QIDQ5198429
Mathew A. Johnson, Kevin Zumbrun
Publication date: 8 August 2011
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0909.1857
generalized Korteweg-de Vries equationKP-II equationperiodic Evans functionKP-I equationnon-standard orientation index
Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Traveling wave solutions (35C07)
Related Items (20)
Transverse instability of line solitary waves in massive Dirac equations ⋮ Counting unstable eigenvalues in Hamiltonian spectral problems via commuting operators ⋮ Transverse dynamics of two-dimensional gravity-capillary periodic water waves ⋮ On the stability of periodic solutions of the generalized Benjamin-Bona-Mahony equation ⋮ On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions ⋮ 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 ⋮ Stability for line solitary waves of Zakharov-Kuznetsov 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 Spectral Stability of Small Periodic Traveling Waves for the KP Equation ⋮ Transverse linear stability of line periodic traveling waves for water-wave models ⋮ Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit
This page was built for publication: Transverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev–Petviashvili Equation