On Fractional Benney Type Systems

TL;DR

This paper develops fractional Benney type systems combining fractional Schrödinger and porous medium equations, proving the existence of weak solutions under certain conditions, advancing the mathematical understanding of wave interactions.

Contribution

It introduces a novel fractional Benney type system and establishes existence results for weak solutions under weak coupling or small initial data.

Findings

Existence of weak solutions for the fractional system

Analysis under weak coupling or small initial data

Extension of classical models to fractional derivatives

Abstract

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 Schr\"odinger equation coupled with a fractional porous medium equation. Under the assumption of weak coupling or small initial data related to the fractional Schr\"odinger equation, it is proved the existence of weak solutions to the Cauchy problem.