John Alberta1 and Jaime Angulo Pavaa2
a1 Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA
a2 Department of Mathematics, IMECC-UNICAMP, CP 6065. CEP 13083-970, Campinas São Paulo, Brazil
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
, we prove the existence and stability of a two-parameter family of ground states associated with a two-parameter family of symmetries.
(Received September 05 2002)
(Accepted March 28 2003)