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

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