Solitons in an extended nonlinear Schr\"odinger equation with third-order dispersion and pseudo-Raman effect

TL;DR

This paper investigates soliton dynamics in an extended nonlinear Schrödinger equation incorporating third-order dispersion, pseudo-Raman effects, and spatial inhomogeneity, revealing conditions for stable wave-number shifts and validating analytical solutions with numerical simulations.

Contribution

It introduces a novel extended NLSE model with pseudo-Raman effects and spatially varying dispersion, analyzing stability and soliton behavior with both analytical and numerical methods.

Findings

Wave-number downshift can be compensated by upshift through spatially increasing SOD.

Stability depends on the sign of the TOD parameter, stable for positive and unstable for negative.

Analytical solutions agree well with numerical simulations.

Abstract

Dynamics of solitons is considered in an extended nonlinear Schr\"odinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, third-order dispersion (TOD) and inhomogeneity of the spatial second-order dispersion (SOD). It is shown that wave-number downshift by the pseudo-SRS may be compensated by upshift provided by spatially increasing SOD with taking into account TOD. The equilibrium state is stable for positive parameter of TOD and unstable for negative one. The analytical solutions are verified by comparison with numerical results