The effect of the fifth-order nonlinearity on the existence of bright solitons below the modulation instability threshold

TL;DR

This paper investigates how adding a fifth-order nonlinear term to high-order nonlinear Schrödinger equations affects bright soliton solutions, revealing only minor amplitude corrections and characterizing these solutions as quasi-solitons.

Contribution

It introduces and analyzes the impact of fifth-order nonlinearity in HONLSE models, showing minimal amplitude change and the quasi-soliton nature of solutions.

Findings

Fifth-order nonlinearity causes small amplitude corrections.

Bright solitons behave as quasi-solitons with fifth-order terms.

The core soliton structure remains largely unchanged.

Abstract

We analyze three different high-order nonlinear Schr\"{o}dinger equation (HONLSE) models that have been used in the literature to describe the evolution of slowly modulated gravity waves on the surface of ideal finite-depth fluid. We demonstrate that the inclusion of the fifth-order nonlinear term to the HONLSE model introduces only a small correction to the amplitude of the bright HONLSE soliton solutions obtained without this term. Such soliton slutions behave as quasi-solitons in this more general case.