Existence of traveling waves for the two-dimensional Zakharov system

TL;DR

This paper constructs small-speed traveling solitary waves for the 2D Zakharov system using a fixed point method and studies their asymptotic properties.

Contribution

It introduces a novel fixed point approach to establish the existence of traveling waves in the 2D Zakharov system for arbitrary small speeds.

Findings

Existence of small-speed traveling solitary waves.

Asymptotic behavior of the constructed waves.

Application of fixed point methods to nonlinear PDEs.

Abstract

Via a fixed point argument, we construct solitary waves for the two-dimensional Zakharov system that travel with any small speed $c \in \mathbb{R}^2$. Moreover, we investigate their asymptotic behavior.