Journal ArticleDOI
A noncompact spin model in (2+1) dimensions
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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.About:
This article is published in Physics Letters B.The article was published on 1990-09-20. It has received 7 citations till now. The article focuses on the topics: Topological quantum number & Spin model.read more
Citations
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Bilinearization of multidimensional topological magnets
TL;DR: In this article, the Hirota bilinear form is used to model the topological properties of magnetic models, such as the Heisenberg ferromagnets and the (2+1)-dimensional O(3) sigma model.
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Gauge equivalence theory of the noncompact Ishimori model and the Davey–Stewartson equation
TL;DR: In this paper, a non-compact version of the Ishimori spin model and the Davey-Stewartson equation are shown to have the same properties, and the role played by the symmetry group associated with the gauge equivalent equations under consideration is clarified.
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Loop algebras and symmetries related to both a compact and a noncompact version of a (2+1)-dimensional spin model
TL;DR: In this article, it was shown that both the compact and noncompact version of a nonlinear spin field system in 2 + 1 dimensions, the so-called Ishimori model, allows an infinite-dimensional Lie algebra with a loop algebra structure.
Journal ArticleDOI
Group theory of a nonlinear spin field model in 2 + 1 dimensions
TL;DR: In this paper, the authors studied both the compact and the noncompact version of an integrable nonlinear spin field system in 2 + 1 dimensions, the so-called Ishimori model, within a group theory framework.
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Equivariant and self-similar standing waves for a Hamiltonian hyperbolic-hyperbolic spin-field system
TL;DR: In this paper, the existence of equivariant standing waves in both regular hyperbolic coordinates as well as similarity variables was proved. But their asymptotic behavior was not studied.
References
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Classical integrable finite-dimensional systems related to Lie algebras
TL;DR: In this article, a review of the results obtained in this field during the last few years is presented, and some new results both of physical and mathematical interest are also presented, as well as some generalizations of these models, naturally suggested by their association with Lie algebras.
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Topology of Higgs fields
TL;DR: In this paper, it was shown that the conserved magnetic charge discovered by ’t Hooft in non−Abelian gauge theories with spontaneous symmetry breaking is not associated with the invariance of the action under a symmetry group.
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On the inverse scattering transform of multidimensional nonlinear equations related to first‐order systems in the plane
TL;DR: In this article, the inverse problem associated with a rather general system of n first-order equations in the plane is linearized by utilizing a Riemann-Hilbert problem; similarly, a DBAR problem is used when the system is elliptic.
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Pole expansions of nonlinear partial differential equations
TL;DR: In this article, the motion of the poles of the Burgers-Hopf equations is shown to correspond formally to the motion for one-dimensional particles interacting via simple two-body potentials, such that the corresponding many-body problems are integrable.