Book ChapterDOI
On Continuous Limits of Some Generalized Compressible Heisenberg Spin Chains
N. S. Serikbaev,Kur. Myrzakul,F. K. Rahimov,Ratbay Myrzakulov +3 more
- Vol. 153, pp 535-542
TLDR
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.read more
Citations
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Journal ArticleDOI
Integrable (2+1)-Dimensional Spin Models with Self-Consistent Potentials
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.
Journal ArticleDOI
Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials
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.
Journal ArticleDOI
Darboux transformation and exact solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials
Z. S. Yersultanova,M. Zhassybayeva,Kuralay Yesmakhanova,Gulgasyl Nugmanova,Ratbay Myrzakulov +4 more
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.
Journal ArticleDOI
Darboux Transformation and Exact Solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials
Z. S. Yersultanova,M. Zhassybayeva,Kuralay Yesmakhanova,Gulgasyl Nugmanova,Ratbay Myrzakulov +4 more
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.
Posted Content
Integrable geometric flows of interacting curves/surfaces, multilayer spin systems and the vector nonlinear Schr\"odinger equation
TL;DR: In this paper, the Lakshmanan equivalent of the nonlinear Schrodinger equation (NLSE) for the integrable multilayer M-LIII equation is presented.
References
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Journal ArticleDOI
Continuum spin system as an exactly solvable dynamical system
TL;DR: In this paper, it was shown that the one-dimensional classical spins with nearest neighbor Heisenberg interaction is an exactly solvable system and its dynamics describable by the nonlinear Schrodinger equation.
Journal ArticleDOI
Motion of curves and surfaces and nonlinear evolution equations in (2+1) dimensions
TL;DR: In this article, it was shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or equivalently, moving surfaces.
Journal ArticleDOI
A (2+1)-dimensional integrable spin model: geometrical and gauge equivalent counterpart, solitons and localized coherent structures
TL;DR: In this paper, a non-isospectra (2 + 1)-dimensional integrable spin equation is investigated and it is shown that its geometrical and gauge equivalent counterparts are the Schrodinger equation belonging to the class of equations discovered by Calogero and discussed by Zakharov and studied recently by Strachan.
Journal ArticleDOI
Gauge equivalence between -dimensional continuous Heisenberg ferromagnetic models and nonlinear Schrödinger-type equations
TL;DR: In this article, the gauge equivalence between the 2C 1/-dimensional Zakharov equation and the.2C 1/dimensional integrable continuous Heisenberg ferromagnetic model is established.
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