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Surfaces and Curves Induced by Nonlinear Schrödinger-Type Equations and Their Spin Systems

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dc.contributor.author Myrzakul, Akbota
dc.contributor.author Nugmanova, Gulgassyl
dc.contributor.author Serikbayev, Nurzhan
dc.contributor.author Myrzakulov, Ratbay
dc.date.accessioned 2024-09-24T12:32:40Z
dc.date.available 2024-09-24T12:32:40Z
dc.date.issued 2021
dc.identifier.citation Myrzakul, A.; Nugmanova, G.; Serikbayev, N.; Myrzakulov, R. Surfaces and Curves Induced by Nonlinear Schrödinger-Type Equations and Their Spin Systems. Symmetry 2021, 13, 1827. https:// doi.org/10.3390/sym13101827 ru
dc.identifier.issn 2548-2297
dc.identifier.other doi.org/10.3390/sym13101827
dc.identifier.uri http://rep.enu.kz/handle/enu/16929
dc.description.abstract In recent years, symmetry in abstract partial differential equations has found wide application in the field of nonlinear integrable equations. The symmetries of the corresponding transformation groups for such equations make it possible to significantly simplify the procedure for establishing equivalence between nonlinear integrable equations from different areas of physics, which in turn open up opportunities to easily find their solutions. In this paper, we study the symmetry between differential geometry of surfaces/curves and some integrable generalized spin systems. In particular, we investigate the gauge and geometrical equivalence between the local/nonlocal nonlinear Schrödinger type equations (NLSE) and the extended continuous Heisenberg ferromagnet equation (HFE) to investigate how nonlocality properties of one system are inherited by the other. First, we consider the space curves induced by the nonlinear Schrödinger-type equations and its equivalent spin systems. Such space curves are governed by the Serret–Frenet equation (SFE) for three basis vectors. We also show that the equation for the third of the basis vectors coincides with the well-known integrable HFE and its generalization. Two other equations for the remaining two vectors give new integrable spin systems. Finally, we investigated the relation between the differential geometry of surfaces and integrable spin systems for the three basis vectors. ru
dc.language.iso en ru
dc.publisher Symmetry ru
dc.relation.ispartofseries 13;1827
dc.subject symmetry in nonlinear integrable equation ru
dc.subject nonlinear Schrödinger equation ru
dc.subject Heisenberg ferromagnet equation ru
dc.subject Chen–Lee–Liu equation ru
dc.subject derivative spin system ru
dc.subject isomorphism of Lie algebras ru
dc.subject soliton solution ru
dc.subject soliton surfaces ru
dc.subject nonlocal integrable equations ru
dc.title Surfaces and Curves Induced by Nonlinear Schrödinger-Type Equations and Their Spin Systems ru
dc.type Article ru


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