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Journal ArticleDOI

Integrable Reductions of Manycomponent Magnetic Systems in (1,1) Dimensions

01 Aug 1983-Physica Scripta (IOP Publishing)-Vol. 28, Iss: 2, pp 229-234
TL;DR: In this article, a generalized many component Heisenberg spin chain with phonon interaction is proposed, which can be reduced to different real magnetic systems such as many chained magnetic crystals with nontrivial interchain couplings, a mixture of many chained ferro and antiferromagnets, etc.
Abstract: A generalized many component Heisenberg spin chain with phonon interaction is proposed Some reductions of the proposed model leading to different real magnetic systems such as many chained magnetic crystals with nontrivial interchain couplings, a mixture of many chained ferro and antiferromagnets, a "colour" generalized Pierels-Hubbard model, etc, are studied It has been shown that the dynamics of all the above real models are close to some integrable systems and coincide with them in certain limits Such integrable systems are the coupled generalised system of Yajima and Oikawa and U(p, q) nonlinear Schrodinger equation, already well studied
Citations
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Journal ArticleDOI
TL;DR: In this paper, it was shown that many sublattice isotropic XY chain with magnon-phonon interactions at the long-wave approximations may be described by generalized Zakharov's system with U(p, q) isogroup.
Abstract: It is shown that many sublattice isotropic XY chain with magnon-phonon interactions at the long-wave approximations may be described by generalized Zakharov's system with U(p, q) isogroup. Two-sublattice XY chain through the Jordan-Wigner transformations reduced to Su-Schriffer-Heeger coupled electron-phonon model in the quasi-one-dimensional conductor polyacetylene (CH)x theory. The Hamiltonian structure of U(p, q) Zakharov's system and its "ultrarelativistic" limit (i.e., the Yajima-Oikawa system with U(p, q) isogroup) are studied. The linear problem and the generating functionals for infinite series of additional integrals of motion for U(p, q) Yajima-Oikawa system are constructed. Four types of soliton solutions under different boundary conditions and appropriate integrals of particles number and energy are found. The quasistationary and ultra-relativistic limits are discussed.

28 citations

Journal ArticleDOI
TL;DR: In this paper, the authors formulate the reduction procedure of the quantum lattice Heisenberg XYZ model to the continuum Landau-Lifshitz model based on generalized coherent states (GCS) of the SU(2) group.
Abstract: On the basis of the method of generalized coherent states (GCS) of the SU(2) group we formulate the reduction procedure of the quantum lattice Heisenberg XYZ model to the continuum Landau-Lifshitz model. The choice of the GCS representation is determined (i) by their proximity to the corresponding classical states and (ii) by similarity of the geometric structure of the homogeneous spaces on which the SU(2) GCS and the vector of the magnetic moment of the corresponding Landau-Lifshitz model are defined. The present reduction procedure is allowed only in the case of weak anisotropy. Accounting for a weak one-ion anisotropy leads to the Landau-Lifshitz model with a renormalized anisotropy tensor. The contribution of such an anisotropy vanishes for the s = 1/2 case.

20 citations

Journal ArticleDOI
TL;DR: In this article, a modified version of the Ishimori model endowed with SU(1,1) symmetry is proposed, and some classes of both rational and biperiodic exact singular solutions are characterized by a topological charge.

7 citations

Posted Content
TL;DR: In this article, the authors studied MNLS related to the DIII-type symmetric spaces and derived new types of 2-component NLS equations, which are counterexamples to the Zakharov-Schulman theorem.
Abstract: We study MNLS related to the DIII-type symmetric spaces Applying to them Mikhailov reduction groups of the type $\mathbb{Z}_r\times \mathbb{Z}_2$ we derive new types of 2-component NLS equations These are {\bf not} counterexamples to the Zakharov-Schulman theorem because the corresponding interaction Hamiltonians depend not only on $|q_k|^2$, but also on $q_1q_2^* +q_1^* q_2$

6 citations

Journal ArticleDOI
TL;DR: In this article, the nonlinear dynamics of a Heisenberg spin chain with an external time-oscillating magnetic field were investigated by applying the Darboux transformation method to the linear eigenvalue problem associated with this equation.
Abstract: In this paper, we investigate the nonlinear dynamics of a Heisenberg spin chain with an external time-oscillating magnetic field. Such dynamics can be described by a Landau–Lifshitz-type equation. We apply the Darboux transformation method to the linear eigenvalue problem associated with this equation, and obtain the multi-soliton solution with a purely algebraic iterative procedure. Through the analytical analysis and graphical illustrations for the solutions obtained, we discuss in detail the effects of an external magnetic field on the nonlinear wave. Under the action of an external field, although the amplitude, width and depth of soliton vary periodically with time and its symmetry property is changeable, the soliton can also propagate stably and it possesses particle-like behavior.

5 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the energy spectra and relaxation coefficients of Goldstone modes of spin waves were studied in a ferrimagnetic semiconductor with arbitrary number n of magnetic sublittices at low temperatures.

1 citations