Damped solitons in an extended nonlinear Schrödinger equation with a spatial stimulated Raman scattering and decreasing dispersion

Abstract

Dynamics of solitons is considered in the framework of an extended nonlinear Schrödinger equation (NLSE), which is derived from a system of the Zakharov's type for the interaction between high-and low-frequency (HF and LF) waves. The resulting NLSE includes a pseudo-stimulatedRaman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term, which is a known ingredient of the temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial second-order dispersion (SOD) and linear losses of HF waves. It is shown that wavenumber downshift by the pseudo-SRS may be compensated by upshift provided by SOD whose local strength is an exponentially decaying function of the coordinate. An analytical soliton solution with a permanent shape is found in an approximate form, and is verified by comparison with numerical results. Keywords: Extended Nonlinear Schrödinger Equation, Damped Soliton Solution, StimulatedScattering, Damping Low-Frequency Waves, Linear Loss High-Frequency Waves, Inhomogeneity Highlights >Dynamics of damped solitons is studied in an extended inhomogeneous nonlinear Schrödinger equation. >We consider media with stimulated-scattering damping acting on low-frequency waves and inhomogeneous spatial dispersion. >An approximate analytical solution for damped solitons is found in an explicit form.

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