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

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dc.contributor Казанский федеральный университет
dc.contributor.author Belashov Vasily Yurievich en
dc.contributor.author Kharshiladze Oleg Avtandilovich en
dc.contributor.author Belashova Elena Semenovna en
dc.date.accessioned 2021-03-23T08:54:45Z
dc.date.available 2021-03-23T08:54:45Z
dc.date.issued 2021
dc.identifier.citation Belashov V.Yu. Dynamics of Solitons of the Generalized Nonlinear Schrödinger Equation in an Inhomogeneous and Nonstationary Medium: Evolution and Interaction / V.Yu. Belashov, O.A. Kharshiladze, E.S. Belashova // Geomagnetism and Aeronomy. - 2021. - Vol. 61, No. 2. - P. 149-157. en
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/163476
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. en
dc.language.iso en
dc.relation.ispartofseries GEOMAGNETISM AND AERONOMY en
dc.rights открытый доступ
dc.subject Soliton
dc.subject dynamics
dc.subject Generalized Nonlinear Schrödinger Equation
dc.subject inhomogeneous and nonstationary media
dc.subject evolution
dc.subject interaction
dc.subject.other Космические исследования
dc.subject.other Математика
dc.subject.other Физика
dc.title Dynamics of Solitons of the Generalized Nonlinear Schrödinger Equation in an Inhomogeneous and Nonstationary Medium: Evolution and Interaction en
dc.type Article
dc.contributor.org Институт физики
dc.description.pages 149-157
dc.relation.ispartofseries-issue 2
dc.relation.ispartofseries-volume 61
dc.pub-id 248850
dc.identifier.doi 10.1134/S0016793221020031


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