Revista Matemática Complutense

, Volume 26, Issue 2, pp 409–426 | Cite as

Convergence of a numerical scheme for a coupled Schrödinger–KdV system

Article

Abstract

We prove the convergence in a strong norm of a finite difference semidiscrete scheme approximating a coupled Schrödinger–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.

Keywords

Nonlinear Schrödinger equation Korteweg–de Vries equation Short wave long wave interaction Finite difference scheme 

Mathematics Subject Classification

35Q55 35Q53 

Notes

Acknowledgements

The authors were supported by the Portuguese Foundation for Science and Technology (FCT), PEst OE/MAT/UI0209/2011, and the FCT grant PTDC/MAT/110613/2009. PA was also supported by FCT through a Ciência 2008 fellowship.

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Copyright information

© Revista Matemática Complutense 2012

Authors and Affiliations

  1. 1.Centro de Matemática e Aplicações Fundamentais and Departamento de MatemáticaFaculdade de Ciências da Universidade de LisboaLisboaPortugal

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