Solitons in a forced nonlinear Schr\"odinger equation with the pseudo-Raman effect

TL;DR

This paper investigates the behavior of solitons in an extended nonlinear Schrödinger equation modeling wind-driven ocean waves, revealing how pseudo-Raman effects influence soliton stability and dynamics.

Contribution

It introduces a novel NLSE with a pseudo-SRS term derived from ocean wave models and analyzes how wind traction can stabilize solitons against convective instability.

Findings

Pseudo-SRS causes wavenumber downshift in solitons.

Wind traction induces an upshift, stabilizing solitons.

Analytical and numerical solutions confirm soliton robustness.

Abstract

Dynamics of solitons is considered in the framework of an extended nonlinear Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped low-frequency (LF) internal waves. The drive gives rise to a convective (but not absolute) instability in the system. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, which is a spatial-domain counterpart of the SRS term, a well-known ingredient of the temporal-domain NLSE in optics. Analysis of the field-momentum balance and direct simulations demonstrate that wavenumber downshift by the pseudo-SRS may be compensated by the upshift induced by the wind traction, thus maintaining robust bright solitons in both stationary and oscillatory forms; in particular, they are not destroyed by the underlying convective instability. Analytical soliton solutions are found in an approximate form and verified by numerical simulations. Solutions for soliton pairs are obtained in the numerical form.