Nonlinear Stability for the Periodic and Non-Periodic Zakharov System

TL;DR

This paper establishes the existence and nonlinear stability of periodic traveling wave solutions, including solitary waves, for the Zakharov system, advancing understanding of its dynamic behavior.

Contribution

It proves the existence of smooth periodic solutions and their nonlinear stability, improving previous results by including solitary wave stability for the Zakharov system.

Findings

Existence of smooth periodic traveling wave solutions.

Nonlinear stability of these solutions under the periodic flow.

Stability of solitary wave solutions associated with the system.

Abstract

We prove the existence of a smooth curve of periodic traveling wave solutions for the Zakharov system. We also show that this type of solutions are nonlinear stable by the periodic flow generated for the system mentioned before. An improvement of the work of Ya Ping is made, we prove the stability of the solitary wave solutions associated to the Zakharov system.