  This work is divided into two parts. First, we analyze the existence of
positive bound and ground states for a second order stationary system coming
from a coupled system of nonlinear Schr\"odinger--Korteweg-de Vries equations.
Second, we extend these results for a higher order system of nonlinear
Schr\"odinger--Korteweg-de Vries equations. Looking for "standing-traveling"
waves we arrive at a bi-harmonic stationary system, for which we prove the
existence and multiplicity of solutions under appropriate conditions on the
parameters.
