Multi-solitary waves for the one-dimensional Zakharov system

TL;DR

This paper proves the existence of multi-solitary wave solutions for the one-dimensional Zakharov system, where each wave travels at a different speed, extending methods from NLS and gKdV equations.

Contribution

It establishes the first known existence of multi-solitary waves with different speeds for the 1D Zakharov system, adapting techniques from related nonlinear equations.

Findings

Existence of solutions asymptotic to multiple solitary waves with distinct speeds.

Extension of methods from NLS and gKdV to the Zakharov system.

Framework for analyzing multi-solitary wave interactions in 1D.

Abstract

Given different speeds $c_1$ , ... , $c_K$, in the present paper we establish the existence of a solution to the Zakharov system in dimension 1 that behaves asymptotically like a $K$-solitary wave, each wave travelling with speed $c_k$. The proof is adapted from previous results for the NLS and gKdV equations.