On long time behavior of solutions of the Schr\"{o}dinger-Korteweg-de Vries system

TL;DR

This paper proves that solutions to the Schrödinger-Korteweg-de Vries system decay to zero over time in the energy space, regardless of integrability or initial size, using recent analytical techniques.

Contribution

It establishes decay results for the Schrödinger-Korteweg-de Vries system without size or integrability restrictions, expanding understanding of long-term behavior.

Findings

Solutions decay to zero in the energy space over time

Decay results are independent of integrability of the system

No size assumptions are required for the decay to occur

Abstract

We are concerned with the decay of long time solutions of the initial value problem associated with the Schr\"odinger-Korteweg-de Vries system. We use recent techniques in order to show that solutions of this system decay to zero in the energy space. The result is independent of the integrability of the equations involved and it does not require any size assumptions.