Convergence of Fourier spectral method for resonant long-short nonlinear wave interaction.

DOI10.1007/s10492-010-0025-5zbMath1224.65234OpenAlexW1991744657MaRDI QIDQ622860

Abdur Rashid, Shakaib Akram

Publication date: 11 February 2011

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/37852

zbMATH Keywords

numerical resultserror estimatesevolution equationssemidiscretizationFourier spectral methodCrank-Nicolson Fourier spectral schemesenergy estimation methodlong-short wave interactionresonance interaction

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) 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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (5)

A <scp>F</scp>ourier pseudospectral method for a generalized improved <scp>B</scp>oussinesq equation ⋮ Error analysis of an implicit spectral scheme applied to the Schrödinger-Benjamin-Ono system ⋮ Higher order dispersive effects in regularized Boussinesq equation ⋮ Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity ⋮ Hermite spectral method for long-short wave equations

Cites Work

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• On the well-posedness of Benney's interaction equation of short and long waves
• Explicit and exact solutions for generalized long-short wave resonance equations with strong nonlinear term
• Formation and Interaction of Sonic-Langmuir Solitons: Inverse Scattering Method
• A General Theory for Interactions Between Short and Long Waves
• The Complete Solution of the Long‐Wave–Short‐Wave Resonance Equations
• On a nonlinear Schrödinger equation arising in the theory of water waves

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