On the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system

TL;DR

This paper investigates the Cauchy problem for the Zakharov-Rubenchik system, focusing on the stability of solitary waves and contributing to the understanding of wave interactions in physical models.

Contribution

It provides new insights into the well-posedness and stability analysis of the Zakharov-Rubenchik system with respect to line solitary waves.

Findings

Analysis of the Cauchy problem in the presence of solitary waves

Results on the transverse stability and instability of line solitary waves

Enhanced understanding of wave interactions in physical models

Abstract

We address various issues concerning the Cauchy problem for the Zakharov-Rubenchik system (known as the Benney-Roskes system in water waves theory), which models the interaction of short and long waves in many physical situations. Motivated by the transverse stability/instability of the one-dimensional solitary wave (line solitary), we study the Cauchy problem in the background of a line solitary wave.