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Existence and stability of ground-state solutions of a Schrödinger—KdV system

Published online by Cambridge University Press:  12 July 2007

John Albert  and
Jaime Angulo Pava
John Albert
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA
Jaime Angulo Pava
Affiliation:
Department of Mathematics, IMECC-UNICAMP, CP 6065. CEP 13083-970, Campinas São Paulo, Brazil
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Abstract

We consider the coupled Schrödinger–Korteweg–de Vries system which arises in various physical contexts as a model for the interaction of long and short nonlinear waves. Ground states of the system are, by definition, minimizers of the energy functional subject to constraints on conserved functionals associated with symmetries of the system. In particular, ground states have a simple time dependence because they propagate via those symmetries. For a range of values of the parameters α, β, γ, δi, ci, we prove the existence and stability of a two-parameter family of ground states associated with a two-parameter family of symmetries.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 5 , October 2003 , pp. 987 - 1029
Copyright
Copyright © Royal Society of Edinburgh 2003

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