A higher order system of some coupled nonlinear Schr\"odinger and   Korteweg-de Vries equations
  We prove existence and multiplicity of bound and ground state solutions, under appropriate conditions on the parameters, for a bi-harmonic stationary system of coupled nonlinear Schr\"odinger--Korteweg-de Vries equations. 
P. Alvarez-Caudevilla, E. Colorado and R. Fabelo
math.AP