Solitons in a forced nonlinear Schrödinger equation with the pseudo-Raman effect
- 29 December 2015
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 92 (6), 062926
- https://doi.org/10.1103/physreve.92.062926
Abstract
The dynamics of solitons is considered in the framework of an extended nonlinear Schrödinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency surface waves in the ocean, coupled to damped low-frequency 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 demonstrates that wave-number 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 are verified by numerical simulations. Solutions for soliton pairs are obtained in the numerical form.Keywords
Funding Information
- National Research University Higher School of Economics (16-01-0002)
This publication has 59 references indexed in Scilit:
- Asymptotic Shallow Water Models for Internal Waves in a Two-Fluid System with a Free SurfaceSIAM Journal on Mathematical Analysis, 2010
- DDF-based all-fiber optical source of femtosecond pulses smoothly tuned in the telecommunication rangeLaser Physics, 2007
- Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibersPhysical Review E, 2004
- Bright matter wave solitons in Bose–Einstein condensatesNew Journal of Physics, 2003
- Long-wave short-wave resonance for nonlinear geometric opticsDuke Mathematical Journal, 2001
- Analytical solution for the modified nonlinear Schrödinger equation describing optical shock formationPhysical Review E, 1998
- Painlevé analysis and bright solitary waves of the higher-order nonlinear Schrödinger equation containing third-order dispersion and self-steepening termPhysical Review E, 1997
- Soliton pulse compression in dispersion-decreasing fiberOptics Letters, 1993
- Dark-soliton dynamics and shock waves induced by the stimulated Raman effect in optical fibersPhysical Review A, 1990
- Compensation of soliton broadening in nonlinear optical fibers with lossOptics Letters, 1987