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Soliton Self-wave Number Downshift Compensation by the Increasing Second-Order Dispersion
P. 1–10.
In press
Dynamics of solitons in the frame of the extended nonlinear Schr¨odinger equation (NSE) taking into account stimulated Raman scattering (SRS) and inhomogeneous second-order dispersion (SOD) is considered. Compensation of soliton Raman self-wave number downshift in media with increasing second-order linear dispersion is shown. Quasi-soliton solution with small wave number spectrum variation, amplitude and extension are found analytically in adiabatic approximation and numerically. The soliton is considered as the equilibrium of SRS and increasing SOD. For dominate SRS soliton wave number spectrum tends to long wave region. For dominate increasing SOD soliton wave number spectrum tends to shortwave region.
Keywords: индуцированное рассеяние Раманарасширенное нелинейное уравнение Шредингераextended nonlinear Schrodinger equationspatial stimulated Raman scatteringdynamics of solitons and quasi-solutionsInhomogeneous second order dispersionдинамика солитонов и квази-солитоновнеоднородность дисперсии второго порядка
Publication based on the results of:
Ruderman M. C., Petrukhin N., Pelinovsky E., Physica Scripta 2022 Vol. 97 No. 7 Article 075206
Westudy the stability of one-dimensional solitons propagating in an anisotropic medium.Wederived
the Kadomtsev-Petviashvili equation for nonlinear waves propagating in an anisotropic medium. By a
proper variable substitution this equation reduces either to the KPI or to the KPII equation. In the
former case solitons are unstable with respect to the normal modes of transverse perturbations, and in
the latter ...
Added: June 17, 2022
Gevorgian A., Kulagin N., Lerman L. et al., Chaos, Solitons and Fractals 2021 Vol. 143 Article 110550
Localized stationary solutions of nonlinear nonlocal Whitham equation with resonance dispersion relation
are considered. The existence of exponentially localized smooth and singular solitons, bound states of the
solitons and localized solutions with oscillating asymptotics is recognized. The velocity spectra of solitons,
in contrast to all other known Whitham equations, appear to be discrete. Asymptotic “quantization rules”
for calculation of ...
Added: December 22, 2020
Gromov E.M., Malomed B. A., Communications in Nonlinear Science and Numerical Simulation 2020 Vol. 85 Article 105220
We introduce a nonlinear Schrödinger equation (NLSE) which combines the pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a non-conservative cubic one with the first spatial derivative, and an external potential, which helps to stabilize solitons against the pseudo-SRS effect. Dynamics of solitons is addressed by means of analytical and numerical methods. The quasi-particle approximation (QPA) for the solitons ...
Added: February 5, 2020
Gromov E., Malomed B., , in: Generalized Models and Non-classical Approaches in Complex Materials 2. Advanced Structured Materials.: Springer, 2018. Ch. 6 P. 119–144.
Dynamics of solitons is considered in the framework of the extended nonlinear Schrödinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves, in which the LF field is subject to diffusive damping. The model may apply to the propagation of HF waves ...
Added: July 19, 2018
Springer, 2018.
Dynamics of solitons is considered in the framework of the extended nonlinear Schrödinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves, in which the LF field is subject to diffusive damping. The model may apply to the propagation of HF waves ...
Added: July 19, 2018
Gromov E., Malomed B. A., Tyutin V. V., Communications in Nonlinear Science and Numerical Simulation 2018 Vol. 54 P. 13–20
The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schrödinger equations, which incorporate the cross-phase modulation, pseudo-stimulated-Raman-scattering (pseudo-SRS), cross-pseudo-SRS, and spatially inhomogeneous second-order dispersion (SOD). The system models co-propagation of electromagnetic waves with orthogonal polarizations in plasmas. It is shown that the soliton's wavenumber ...
Added: May 18, 2017
Pelinovsky E., Slunyaev A. V., Physical Review Letters 2016 Vol. 117 No. 21 P. 214501
The role of multiple soliton and breather interactions in the formation of very high waves is disclosed
within the framework of the integrable modified Korteweg–de Vries (MKdV) equation. Optimal conditions
for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate
polarities evolve to huge strongly localized transient waves. The focused wave amplitude ...
Added: February 26, 2017
Aseeva N., Blyakhman L. G., Gromov E. et al., / Series Working papers by Cornell University "Physics:Nonlinear Physics, Pattern and Solitons "arxiv.org"". 2016. No. 1602.08572.
Dynamics of solitons is considered in an extended nonlinear Schrödinger 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 ...
Added: February 27, 2016
Aseeva N.V., Gromov E.M., Tyutin V. V., Journal of Experimental and Theoretical Physics 2015 Vol. 121 No. 6 P. 955–960
The dynamics of high-frequency field solitons is considered using the extended nonhomogeneous nonlinear Schrodinger equation with induced scattering from damped low-frequency waves (pseudoinduced scattering). This scattering is a 3D analog of the stimulated Raman scattering from temporal spatially homogeneous damped low-frequency modes, which is well known in optics. Spatial inhomogeneities of second-order linear dispersion and ...
Added: August 18, 2015
Aseeva N., Gromov E., Tyutin V. V., Журнал экспериментальной и теоретической физики 2015 Т. 148 № 6 С. 1092–1097
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 ...
Added: July 31, 2015
Aseeva N.V., Gromov E.M., Tyutin V.V., Radiophysics and Quantum Electronics 2015 Vol. 58 No. 3 P. 209–215
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 ...
Added: May 7, 2015
Aseeva N., Gromov E., Tyutin V. V., Известия высших учебных заведений. Радиофизика 2015 Т. 58 № 3 С. 227–234
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 ...
Added: December 9, 2014
Gromov E., Journal of Physics: Conference Series 2015 Vol. 574 P. 012032
Dynamics of solitons is considered in an extended nonlinear Schrödinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, nonlinear dispersion 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 nonlinear ...
Added: September 11, 2014
Gromov E., Tyutin V. V., Radiophysics and Quantum Electronics 2014 Vol. 57 No. 4 P. 279–286
The stationary waves with nonlinear phase modulation in an extended nonlinear Schrödinger equation with nonlinear dispersion and stimulated Raman–scattering terms are considered. New class of a kink–waves are found. This waves exists as the result of balance of the stimulated Raman–scattering and nonlinear dispersion ...
Added: July 28, 2014