Coupled solitons of intense high-frequency and low-frequency waves in Zakharov-type systems

TL;DR

This paper derives exact coupled soliton solutions in Zakharov-type models for high-frequency and low-frequency wave interactions, analyzing their stability and collision behaviors through analytical and numerical methods.

Contribution

It introduces a new class of two-component solitary-wave solutions in Zakharov-type systems, extending single-component solitons to coupled HF and LF wave interactions.

Findings

Coupled solitons are stable when the LF component acts as a potential well.

Unstable when the LF component forms a barrier, leading to splitting.

In-phase solitons tend to merge, out-of-phase solitons interact elastically.

Abstract

One-parameter families of exact two-component solitary-wave solutions for interacting high-frequency (HF) and low-frequency (LF) waves are found in the framework of Zakharov-type models, which couple the nonlinear Schr\"odinger equation (NLSE) for intense HF waves to the Boussinesq (Bq) or Korteweg - de Vries (KdV) equation for the LF component through quadratic terms. The systems apply, in particular, to the interaction of surface (HF) and internal (LF) waves in stratified fluids. These solutions are two-component generalizations of the single-component Bq and KdV solitons. Perturbed dynamics and stability of the solitary waves are studied in detail by means of analytical and numerical methods. Essentially, they are stable against separation of the HF and LF components if the latter one is shaped as a potential well acting on the HF field, and unstable, against splitting of the two components, with a barrier-shaped LF one. Collisions between the solitary waves are studied by means of direct simulations, demonstrating a trend to merger of in-phase solitons, and elastic interactions of out-of-phase ones.