CONVERGENCE OF NUMERICAL SCHEMES FOR SHORT WAVE LONG WAVE INTERACTION EQUATIONS

DOI10.1142/S0219891611002573zbMath1246.35047arXiv0912.2027OpenAlexW3101926638MaRDI QIDQ2891099

M. S. Figueira, Paulo Amorim

Publication date: 13 June 2012

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.2027

zbMATH Keywords

Cauchy problemcompensated compactnessconvergence proofLax-Friedrichs-schemesemi-implicit Crank-Nichelson scheme

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (3)

The linear stability of shock waves for the nonlinear Schrödinger-inviscid Burgers system ⋮ Convergence of semi-discrete approximations of Benney equations ⋮ A nonlinear model describing a short wave–long wave interaction in a viscoelastic medium

Cites Work

• Numerical computations for long-wave short-wave interaction equations in semi-classical limit
• Convergence of semi-discrete approximations of Benney equations
• Convergence of approximate solutions to conservation laws
• Interaction equations for short and long dispersive waves
• Dispersive properties of a viscous numerical scheme for the Schrödinger equation
• Well-posedness for the Schrödinger-Korteweg-de Vries system
• EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS
• A General Theory for Interactions Between Short and Long Waves
• Well-posedness of the cauchy problem for the long wave-short wave resonance equations
• Equilibrium schemes for scalar conservation laws with stiff sources
• On a nonlinear Schrödinger equation arising in the theory of water waves

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