Communications in Mathematical Analysis

Soliton Dynamics in an Extended Nonlinear Schrodinger Equation with Inhomogeneous Dispersion and Self-phase Modulation

N. V. Aseeva, E. M. Gromov, B. A. Malomed, and V. V. Tyutin

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Abstract

Evolution of solitons is addressed in the framework of an extended nonlinear Schrödinger equation (NLSE), including a pseudo-stimulated-Raman-scattering (pseudo-SRS) 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. In the present context, it is induced by the underlying interaction of the high-frequency envelope wave with a damped lowfrequency wave mode. Also included are spatial inhomogeneity of both the second-order dispersion (SOD) and self-phase modulation (SPM). It is shown that the wavenumber downshift of solitons, caused by the pseudo-SRS, may be compensated by an upshift provided by the increasing SPM and SOD coefficients. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well.

Article information

Source
Commun. Math. Anal., Volume 17, Number 2 (2014), 1-13.

Dates
First available in Project Euclid: 18 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.cma/1418919751

Mathematical Reviews number (MathSciNet)
MR3292955

Zentralblatt MATH identifier
1321.35187

Subjects
Primary: 35Q51: Soliton-like equations [See also 37K40]

Keywords
Extended Nonlinear Schrodinger Equation Soliton Solutions Stimulated Scattering Damped Low-Frequency Waves Inhomogeneity Second-Order Dispersion Self- Phase Modulation Analytical Solutions

Citation

Aseeva, N. V.; Gromov, E. M.; Malomed, B. A.; Tyutin, V. V. Soliton Dynamics in an Extended Nonlinear Schrodinger Equation with Inhomogeneous Dispersion and Self-phase Modulation. Commun. Math. Anal. 17 (2014), no. 2, 1--13. https://projecteuclid.org/euclid.cma/1418919751


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