New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System

Abstract

In this work, we prove that the initial value problem for the Schrödinger–Korteweg–de Vries (SKdV) system is locally well posed in Gevrey spaces for s>−34 and k≥0. This advancement extends recent findings regarding the well posedness of this model within Sobolev spaces and investigates the regularity properties of its solutions.

Keywords

• analytic Gevrey spaces
• well posedness
• coupled system
• Schrödinger equation
• Korteweg–de Vries equation
• regularity