Convergence of a numerical scheme for a coupled Schrödinger–KdV system
Copyright policy )Convergence of a numerical scheme for a coupled Schrödinger–KdV system
We prove the convergence in a strong norm of a finite difference semi-discrete scheme approximating a coupled Schr\"odinger--KdV system on a bounded domain. This system models the interaction of short and long waves. Since the energy estimates available in the continuous case do not carry over to the discrete setting, we rely on a suitably truncated problem which we prove reduces to the original one. We present some numerical examples to illustrate our convergence result.
- University of Lisbon Portugal
NLS equations (nonlinear Schrödinger equations), Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), Finite difference methods for initial value and initial-boundary value problems involving PDEs, Korteweg-de Vries equation, short wave long wave interaction, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, nonlinear Schrödinger equation, finite difference scheme
NLS equations (nonlinear Schrödinger equations), Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), Finite difference methods for initial value and initial-boundary value problems involving PDEs, Korteweg-de Vries equation, short wave long wave interaction, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, nonlinear Schrödinger equation, finite difference scheme
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