Stability of some stationary solutions for the forced KdV equation

DOI10.1016/0167-2789(91)90240-AzbMath0742.35053OpenAlexW1992633840MaRDI QIDQ1181181

Theodore Yao-Tsu Wu, Roberto Camassa

Publication date: 27 June 1992

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

Full work available at URL: https://doi.org/10.1016/0167-2789(91)90240-a

zbMATH Keywords

linear stability analysisperturbation techniquesupercritical forcing distribution

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) General topics in linear spectral theory for PDEs (35P05)

Related Items (12)

A locally conservative eulerian-Lagrangian finite difference method for the forced KdV equation ⋮ Numerical algorithms for water waves with background flow over obstacles and topography ⋮ The hyperbolic relaxation systems for the forced KdV equations with hydraulic falls ⋮ A stability analysis of periodic solutions to the steady forced Korteweg-de Vries-Burgers equation ⋮ The wave stability of solitary waves over a bump for the full Euler equations ⋮ A study of wave trapping between two obstacles in the forced Korteweg-de Vries equation ⋮ Numerical stability of symmetric solitary-wave-like waves of a two-layer fluid -- forced modified KdV equation ⋮ Stability of some stationary solutions to the forced KdV equation with one or two bumps ⋮ Forced nonlinear disturbances in incompressible boundary layers ⋮ Supercritical surface gravity waves generated by a positive forcing ⋮ Near-critical turbulent open-channel flows over bumps and ramps ⋮ A simple and robust boundary treatment for the forced Korteweg-de Vries equation

Cites Work

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• Transient waves produced by flow past a bump
• Interaction of a moving dipole with a soliton in the KdV equation
• Perturbation methods in applied mathematics
• Nonlinear stability of fluid and plasma equilibria
• On the excitation of long nonlinear water waves by a moving pressure distribution
• Soliton generation and nonlinear wave propagation
• Generation of upstream advancing solitons by moving disturbances
• Stability of forced steady solitary waves
• Resonant flow of a stratified fluid over topography
• Model equations for long waves in nonlinear dispersive systems

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