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

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.