Integrable Reductions of Manycomponent Magnetic Systems in (1,1) Dimensions
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
More filters
TL;DR: In this article, the many component magnetic system given by Makhankov et al. is reduced to a quanum nonlinear Schrodinger model without the U(p, q) symmetry.
Abstract: In this comment, the many component magnetic system given by Makhankov et al. [1] is reduced to a quanum nonlinear Schrodinger model without the U(p, q) symmetry. For the ferro- and antiferromagnetic system this model is completely integrable and the bound states of the model are discussed.
2 citations
TL;DR: In this paper, a generalization of the U(p, q) system (0.1) that takes into account a spin-spin interaction is obtained, and an exact solitonlike solution for it is given.
Abstract: A vector generalization of the system (0.1) to be the multicomponent Heisenberg XXZ model is derived. The Hamiltonian structure is discussed. A large class of exact soliton (regular and singular) solutions is obtained for the U(p, q) generalization of the system (0.1) and the associated U(N) nonlinear Schroedinger equation and Zakharov's systems of equations. For the U(2) and U(1, 1) versions, the regions of existence of single-soliton solutions on the (..cap alpha.., ..beta..) plane are found. A generalization of the U(p, q) system (0.1) that takes into account a spin-spin interaction is obtained, and an exact solitonlike solution for it is given. The energy spectrum on some of the obtained solutions is calculated.
TL;DR: In this article, a multicomponent coupled spin model, which is equivalent to a generalized Hubbard model, is solved by the Bethe ansatz method, and it is shown to be the multic-component fermionic nonlinear Schrodinger model.
01 Jan 1999
TL;DR: In this paper, the authors investigated the nonlinear properties of magnet crystals and their applications in the field of applied science and technology and applied them to the theory of nonlinear differential equations (such as inverse scattering method, algebraic and geometrical methods, integrating, numerical experiments and so on).
Abstract: Investigation of nonlinear properties of magnet crystals attracts a great attention in the past decades [1-10]. Mainly, this interest has been initiated both by rapid development of the theory of nonlinear differential equations (such branches as inverse scattering method, algebraic and geometrical methods, of integrating, numerical experiments and so on), new experimental data, and the possibility of their wide application in the different branches of applied science and technology.
01 Jan 1990
TL;DR: In this article, the authors give a list of nonlinear differential equations and their localized solutions (quasi-solitons) which, along with the KdV equation, often occur in various physical applications.
Abstract: In this short chapter we give a list of nonlinear differential equations and their localized solutions (quasi-solitons) which, along with the KdV equation, often occur in various physical applications. This list is not complete of course. It is still being expanded, however sufficiently simple equations presented in the following can be used as mathematical models of quite different, in nature, physical systems. In this sense, and due to the mathematical properties of some of them, they fulfil the same role in the theory of nonlinear differential equations as do elliptic, parabolic and wave equations in the theory of linear partial differential equations and are therefore universal.
References
More filters
TL;DR: In this article, a review of the theoretical and experimental results obtained on simple magnetic model systems on magnetic lattices of dimensionality 1, 2, and 3 is presented, with particular attention paid to the approximation of these model systems in real crystals, viz how they can be realized or be expected to exist in nature.
Abstract: “…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will a...
1,570 citations
TL;DR: In this article, the authors studied thermodynamic and some dynamic properties of a one-dimensional model system whose displacement field Hamiltonian is strongly anharmonic, and is representative of those used to study displacive phase transitions.
Abstract: We have studied thermodynamic and some dynamic properties of a one-dimensional-model system whose displacement field Hamiltonian is strongly anharmonic, and is representative of those used to study displacive phase transitions. By studying the classical equations of motion, we find important solutions (domain walls) which cannot be represented effectively by the usual phonon perturbation expansions. The thermodynamic properties of this system can be calculated exactly by functional integral methods. No Hartree or decoupling approximations are made nor is a temperature dependence of the Hamiltonian introduced artificially. At low temperature, the thermodynamic behavior agrees with that found from a phenomenological model in which both phonons and domain walls are included as elementary excitations. We then show that equal-time correlation functions calculated by both functional-integral and phenomenological methods agree, and that the dynamic correlation functions (calculated only phenomenologically) exhibit a spectrum with both phonon peaks and a central peak due to domain-wall motion.
685 citations
TL;DR: A survey of the properties of soliton-type solutions to non-linear wave equations appearing in various fields of physics is given in this paper, where the results of computer experiments on the dynamics of the formation and interaction (in one-space-dimensional geometry) of solit-type objects are presented at length.
499 citations
300 citations