The initial-boundary value problem for Schr\"odinger-Korteweg-de Vries system on the half-line

TL;DR

This paper establishes local well-posedness for the Schr"odinger-Korteweg-de Vries system on half-lines using boundary forcing operators, advancing understanding of low regularity solutions for this coupled PDE system.

Contribution

It introduces a novel approach combining two families of boundary forcing operators to prove well-posedness in low regularity settings for the IBVP.

Findings

Proved local well-posedness for Schr"odinger-Korteweg-de Vries system on half-lines.

Utilized boundary forcing operators developed by Holmer and Cavalcante.

Extended low regularity analysis techniques to coupled PDE systems.

Abstract

We prove local well-posedness for the initial-boundary value problem (IBVP) associated to the Schr\"odinger-Korteweg de Vries system on right and left half-lines. The results are obtained in the low regularity setting by using two analytic families of boundary forcing operators, being one of these family developed by Holmer to study the IBVP associated to the Korteweg-de Vries equation (Communications in Partial Differential Equations, 31 (2006)) and the other family one was recently introduced by Cavalcante (Differential and Integral Equations (2017)) in the context of nonlinear Schr\"odinger with quadratic nonlinearities.