Well-posedness for the 1D Zakharov-Rubenchik system

TL;DR

This paper establishes local and global well-posedness for the 1D Zakharov-Rubenchik system, identifying sharp conditions and analyzing solution norm growth, thus advancing understanding of this coupled PDE system.

Contribution

It provides new well-posedness results for the 1D Zakharov-Rubenchik system and demonstrates sharpness through ill-posedness results, using innovative methods from classical Zakharov systems.

Findings

Well-posedness results for the 1D Zakharov-Rubenchik system

Ill-posedness results indicating sharpness of conditions

Analysis of solution norm growth over time

Abstract

Local and global well-posedness results are established for the initial value problem associated to the 1D Zakharov-Rubenchik system. We show that our results are sharp in some situations by proving Ill-posedness results otherwise. The global results allow us to study the norm growth of solutions corresponding to the Schrodinger equation term. We use ideas recently introduced to study the classical Zakharov systems.