 
Summary: Existence and stability of groundstate solutions of
a SchršodingerKdV system
John Albert
Department of Mathematics
University of Oklahoma
Norman, OK 73019
Jaime Angulo Pava
Department of Mathematics
IMECCUNICAMP
C.P. 6065. CEP 13083970
Campinas S~ao Paulo, Brazil
We consider the coupled SchršodingerKdV system
i(ut + c1ux) + 1uxx = uv
vt + c2vx + 2vxxx + (v2)x = (u2)x,
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 , , , i, ci, we prove the existence and stability of a twoparameter
