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

Optics Communications. 2014. Vol. 320. P. 88–93.

Gromov E.M., Malomed B. A.

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-stimulated-Raman-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: расширенное нелинейное уравнение Шредингера, inhomogeneity, неоднородность дисперсии второго порядка, Stimulated Scattering, Damping Low-Frequency Waves, индуцированное рассеяние, extended nonlinear Schrödinger equation, Damped Soliton Solution, Linear Loss High-Frequency Waves, Inhomogeneity second order dispersion, затухающее солитонное решение, затухающие низко частотные волны, линейные потери высокочастотных волн

Publication based on the results of: Новые солитонные решения расширенного нелинейного уравнения Шредингера с пространственным индуцированным рассеянием на затухающих низкочастотных волнах (2014)