KFU. Card publication. Dynamics of Solitons of the Generalized Nonlinear Schrödinger Equation in an Inhomogeneous and Nonstationary Medium: Evolution and Interaction

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DYNAMICS OF SOLITONS OF THE GENERALIZED NONLINEAR SCHRöDINGER EQUATION IN AN INHOMOGENEOUS AND NONSTATIONARY MEDIUM: EVOLUTION AND INTERACTION

Form of presentation

Articles in international journals and collections

Year of publication

2021

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Authors, employees of KFU

Belashov Vasiliy Yurevich, author

Other authors

Kharshiladze Oleg Avtandilovich, author

Belashova Elena Semenovna, author

Bibliographic description in the original language

Belashov V.Yu., Kharshiladze O.A., Belashova E.S. Dynamics of Solitons of the Generalized Nonlinear Schrödinger Equation in an Inhomogeneous and Nonstationary Medium: Evolution and Interaction // Geomagnetism and Aeronomy, 2021, Vol. 61, No. 2, pp. 149–157.

Annotation

The stability and dynamics of the interaction of soliton-like solutions of the generalized nonlinear Schrödinger (NLS) equation describing the dynamics of the envelope of modulated nonlinear waves and pulses (including the phenomenon of wave collapse and the self-focusing of wave beams) in plasma (including space one), as well as in nonlinear optical systems, have been studied with allowance for the inhomogeneity and nonstationarity of the distribution environment. The equation is also used in other areas of physics, such as the theory of superconductivity and low-temperature physics, small-amplitude gravitational waves on the surface of a deep inviscid fluid, etc. It should be noted that the studied equation is not completely integrable, and its analytical solutions are generally unknown (except, perhaps, for smooth solutions of the solitary wave type). However, approaches that were developed earlier for other equations (the generalized Kadomtsev–Petviashvili equation and the three-dimensional NLS equation with the derivative of the nonlinear term) of the Belashov–Karpman system makes it possible to analyze the stability of possible solutions of the these equations and to conduct a numerical study of the dynamics of soliton interaction. This approach is implemented in the study. Sufficient conditions for the stability of two- and three-dimensional soliton-like solutions are obtained analytically, and the cases of stable and unstable (with the formation of breathers) evolution of pulses of various shapes, as well as the interaction of two- and three-pulse structures, which leads to the formation of stable and unstable solutions, were studied numerically. The results can be useful in numerous applications for the physics of ionospheric and magnetospheric plasma and in many other areas of physics.

Keywords

Soliton, dynamics, Generalized Nonlinear Schrödinger Equation, inhomogeneous and nonstationary media, evolution, interaction

The name of the journal

GEOMAGNETISM AND AERONOMY

On-line resource for training course

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/163476/F_GeoMag2102003Belashov.pdf?sequence=1&isAllowed=y

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=248850&p_lang=2

Resource files

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Full metadata record

Field DC	Value	Language
dc.contributor.author	Belashov Vasiliy Yurevich	ru_RU
dc.contributor.author	Kharshiladze Oleg Avtandilovich	ru_RU
dc.contributor.author	Belashova Elena Semenovna	ru_RU
dc.date.accessioned	2021-01-01T00:00:00Z	ru_RU
dc.date.available	2021-01-01T00:00:00Z	ru_RU
dc.date.issued	2021	ru_RU
dc.identifier.citation	Belashov V.Yu., Kharshiladze O.A., Belashova E.S. Dynamics of Solitons of the Generalized Nonlinear Schrödinger Equation in an Inhomogeneous and Nonstationary Medium: Evolution and Interaction // Geomagnetism and Aeronomy, 2021, Vol. 61, No. 2, pp. 149–157.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=248850&p_lang=2	ru_RU
dc.description.abstract	GEOMAGNETISM AND AERONOMY	ru_RU
dc.description.abstract	The stability and dynamics of the interaction of soliton-like solutions of the generalized nonlinear Schrödinger (NLS) equation describing the dynamics of the envelope of modulated nonlinear waves and pulses (including the phenomenon of wave collapse and the self-focusing of wave beams) in plasma (including space one), as well as in nonlinear optical systems, have been studied with allowance for the inhomogeneity and nonstationarity of the distribution environment. The equation is also used in other areas of physics, such as the theory of superconductivity and low-temperature physics, small-amplitude gravitational waves on the surface of a deep inviscid fluid, etc. It should be noted that the studied equation is not completely integrable, and its analytical solutions are generally unknown (except, perhaps, for smooth solutions of the solitary wave type). However, approaches that were developed earlier for other equations (the generalized Kadomtsev–Petviashvili equation and the three-dimensional NLS equation with the derivative of the nonlinear term) of the Belashov–Karpman system makes it possible to analyze the stability of possible solutions of the these equations and to conduct a numerical study of the dynamics of soliton interaction. This approach is implemented in the study. Sufficient conditions for the stability of two- and three-dimensional soliton-like solutions are obtained analytically, and the cases of stable and unstable (with the formation of breathers) evolution of pulses of various shapes, as well as the interaction of two- and three-pulse structures, which leads to the formation of stable and unstable solutions, were studied numerically. The results can be useful in numerous applications for the physics of ionospheric and magnetospheric plasma and in many other areas of physics.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Soliton	ru_RU
dc.subject	dynamics	ru_RU
dc.subject	Generalized Nonlinear Schrödinger Equation	ru_RU
dc.subject	inhomogeneous and nonstationary media	ru_RU
dc.subject	evolution	ru_RU
dc.subject	interaction	ru_RU
dc.title	Dynamics of Solitons of the Generalized Nonlinear Schrödinger Equation in an Inhomogeneous and Nonstationary Medium: Evolution and Interaction	ru_RU
dc.type	Articles in international journals and collections	ru_RU