Local well-posedness for the Zakharov system on the background of a line soliton

TL;DR

This paper establishes local well-posedness for the 2D Zakharov system near a line soliton and demonstrates weak convergence to a nonlinear Schrödinger equation, advancing understanding of wave interactions.

Contribution

It introduces a novel analysis of the Zakharov system with line soliton background and proves weak convergence to NLS, which is a new insight in wave dynamics.

Findings

Local well-posedness for initial data near a line soliton

Weak convergence to nonlinear Schrödinger equation

Enhanced understanding of wave interactions in Zakharov system

Abstract

We prove that the Cauchy problem for the two-dimensional Zakharov system is locally well-posed for initial data which are localized perturbations of a line solitary wave. Furthermore, for this Zakharov system, we prove weak convergence to a nonlinear Schr\"odinger equation.