  We consider the high-order nonlinear Schr\"odinger equation derived earlier
by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope
of slowly modulated gravity waves on the surface of finite-depth irrotational,
inviscid, and incompressible fluid with flat bottom. This equation takes into
account the third-order dispersion and cubic nonlinear dispersive terms. We
rewrite this equation in dimensionless form featuring only one dimensionless
parameter $kh$, where $k$ is the carrier wavenumber and $h$ is the undisturbed
fluid depth. We show that one-soliton solutions of the classical nonlinear
Schr\"{o}dinger equation are transformed into quasi-soliton solutions with
slowly varying amplitude when the high-order terms are taken into
consideration. These quasi-soliton solutions represent the secondary
modulations of gravity waves.
