Author
N. S. Serikbaev
Bio: N. S. Serikbaev is an academic researcher. The author has contributed to research in topics: Spin-½. The author has an hindex of 2, co-authored 2 publications receiving 51 citations.
Topics: Spin-½
Papers
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01 Jan 2004
TL;DR: In this article, the Lakshmanan equivalent counterpart of one of the obtained continuous Heisenberg ferromagnet equation is constructed using the methods of differential geometry of surfaces, and the continuous limits of some generalized compressible Heisenburg spin chains are found.
Abstract: We study the connection between some lattice and continuous Heisenberg spin models. The continuous limits of some generalized compressible Heisenberg spin chains are found. Using the methods of differential geometry of surfaces, the Lakshmanan equivalent counterpart of one of the obtained continuous Heisenberg ferromagnet equation is constructed.
26 citations
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01 Jan 2004
TL;DR: A new class of two-dimensional surfaces generated by formulas which are generalizations of the well known Lelieuvre and Schief formulas is presented in this paper, which are connected with 2D spin systems which are stationary versions of the (2+1)-dimensional classical continuous Heisenberg ferromagnets.
Abstract: A new class of two-dimensional surfaces generated by formulas which are generalizations of the well known Lelieuvre and Schief formulas is presented. These surfaces are connected with two-dimensional spin systems which are stationary versions of the (2+1)-dimensional classical continuous Heisenberg ferromagnets.
25 citations
Cited by
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TL;DR: This paper identifies three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential,, or both, and deduces the equivalent nonlinear Schrodinger family of equations.
Abstract: Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schr\"odinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schr\"odinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schr\"odinger--Hirota--Maxwell--Bloch equations, along with their Lax pairs.
65 citations
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TL;DR: In this article, a general situation in which the curves evolve in the presence of additional selfconsistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials.
40 citations
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TL;DR: In this paper, the Schrodinger-Hirota-Maxwell-Bloch equations were derived in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential or vector potential, or both.
Abstract: Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrodinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schrodinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schrodinger–Hirota–Maxwell–Bloch equations, along with their Lax pairs.
34 citations
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TL;DR: In this paper, the Darboux transformation of the M-XCIX equation is constructed using the DT and a 1-soliton solution of the XCIX is presented.
Abstract: Integrable Heisenberg ferromagnetic equations are an important subclass of integrable systems. The M-XCIX equation is one of a generalizations of the Heisenberg ferromagnetic equation and are integrable. In this paper, the Darboux transformation of the M-XCIX equation is constructed. Using the DT, a 1-soliton solution of the M-XCIX equation is presented.
29 citations
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TL;DR: In this article, the Darboux transformation of the M-XCIX equation is constructed using the DT and a 1-soliton solution of the XCIX is presented.
Abstract: Integrable Heisenberg ferromagnetic equations are an important subclass of integrable systems. The M-XCIX equation is one of a generalizations of the Heisenberg ferromagnetic equation and are integrable. In this paper, the Darboux transformation of the M-XCIX equation is constructed. Using the DT, a 1-soliton solution of the M-XCIX equation is presented.
16 citations