Soliton dynamics in an extended nonlinear Schrodinger equation with a spatial counterpart of the stimulated Raman scattering

TL;DR

This paper investigates soliton behavior in an extended nonlinear Schrödinger equation incorporating a spatial stimulated Raman scattering term and inhomogeneous diffraction, revealing a balance mechanism between wavenumber shifts.

Contribution

It introduces a novel extended NLSE with a spatial SRS term and inhomogeneous diffraction, providing analytical solutions and demonstrating soliton wavenumber compensation.

Findings

Wavenumber downshift caused by PSRS can be compensated by SOD.

Analytical and numerical results show good agreement.

Balance between PSRS and inhomogeneous SOD stabilizes solitons.

Abstract

Dynamics of solitons is considered in the framework of the extended nonlinear Schrodinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves, in which the LF field is subject to diffusive damping. The model may apply to the propagation of HF waves in plasmas. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (PSRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as an ingredient of the temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial second-order diffraction (SOD). It is shown that the wavenumber downshift of solitons, caused by the PSRS, may be compensated by an upshift provided by the SOD whose coefficient is a linear function of the coordinate. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well, including the predicted balance between the PSRS and the linearly inhomogeneous SOD.