On Fractional Benney Type Systems

This paper introduces fractional type evolutionary equations modeling the interaction between short waves and long waves. We consider a fractional Benney type system, which is given by a fractional Schrödinger equation coupled with a fractional porous medium equation. Under the assumption of weak coupling or small initial data related to the fractional Schrödinger equation, it is proved the existence of weak solutions to the Cauchy problem.