Modulational instability in nonlinear nonlocal equations of regularized long wave type

DOI10.1016/j.physd.2016.03.005zbMath1364.76029arXiv1510.04717OpenAlexW2963201818MaRDI QIDQ2357613

Ashish Kumar Pandey, Vera Mikyoung Hur

Publication date: 14 June 2017

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.04717

zbMATH Keywords

modulational instabilityBoussinesqregularized long waveBBMfractional dispersionnonlinear nonlocal

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Traveling wave solutions (35C07)

Related Items (18)

Modulational instability in nonlinear nonlocal equations of regularized long wave type ⋮ Shallow water models with constant vorticity ⋮ High-frequency instabilities of the Ostrovsky equation ⋮ Superharmonic instability for regularized long-wave models* ⋮ Modulational instability in the full-dispersion Camassa–Holm equation ⋮ Modulational instability in the Whitham equation with surface tension and vorticity ⋮ Proof of Modulational Instability of Stokes Waves in Deep Water ⋮ Benjamin-Feir instability of Stokes waves in finite depth ⋮ On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation ⋮ Hyperbolicity study of the modulation equations for the Benjamin–Bona–Mahony equation ⋮ Transverse spectral instabilities in Konopelchenko–Dubrovsky equation ⋮ Stokes waves at the critical depth are modulationally unstable ⋮ Nonlinear modulational instability of dispersive PDE models ⋮ High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs ⋮ The effects of surface tension on modulational instability in full-dispersion water-wave models ⋮ Modulational instability in a full‐dispersion shallow water model ⋮ Full description of Benjamin-Feir instability of Stokes waves in deep water ⋮ Singular solutions of the BBM equation: analytical and numerical study

Cites Work

• On the stability of periodic solutions of the generalized Benjamin-Bona-Mahony equation
• Modulational instability in the Whitham equation with surface tension and vorticity
• On the formation of singularities for surface water waves
• Wave breaking in the Whitham equation
• Modulational instability in nonlinear nonlocal equations of regularized long wave type
• Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
• Modulational Instability and Variational Structure
• Modulational Instability in the Whitham Equation for Water Waves
• Non-linear dispersive waves
• The disintegration of wave trains on deep water Part 1. Theory
• Non-linear dispersion of water waves
• Model equations for long waves in nonlinear dispersive systems
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