TY - JOUR

T1 - Soliton dynamics in an extended nonlinear Schrödinger equation with inhomogeneous dispersion and self-phase modulation

AU - Aseeva, N. V.

AU - Gromov, E. M.

AU - Malomed, B. A.

AU - Tyutin, V. V.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Analytical solutions

KW - Damped low-frequency waves

KW - Extended nonlinear Schrödinger equation

KW - Inhomogeneity

KW - Second-order dispersion

KW - Self-phase modulation

KW - Soliton solutions

KW - Stimulated scattering

UR - http://www.scopus.com/inward/record.url?scp=84919691216&partnerID=8YFLogxK

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AN - SCOPUS:84919691216

SN - 1938-9787

VL - 17

SP - 1

EP - 13

JO - Communications in Mathematical Analysis

JF - Communications in Mathematical Analysis

IS - 2

ER -