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Scattering of localized solitons in the plane
Abstract Localized (exponentially decaying in all directions) soliton solutions of the evolution equations related to the Zakharov-Shabat spectral problem in the plane are explicitly given. They canExpand
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Analysis and applications of the symmetry group of the multidimensional three-wave resonant interaction problem
Abstract The Lie algebra of the symmetry group of the three-wave resonant interaction system in three (or more) space dimensions is shown to be infinite-dimensional and to have the structure of theExpand
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Exotic Galilean Symmetry and Non-Commutative Mechanics ?
Some aspects of the "exotic" particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting positionExpand
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Berry Phase Correction to Electron Density in Solids and
Recent results on the semiclassical dynamics of an electron in a solid are explained using techniques developed for ``exotic'' Galilean dynamics. The system is indeed Hamiltonian and Liouville'sExpand
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On topological soliton dynamics in multidimensional ferromagnetic continuum
A multidimensional model for a ferromagnetic continuum with hydrodynamical properties, which can be regarded as a modified Landau-Lifshitz equation, is presented. The treatment of some physicalExpand
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Structure preserving discretizations of the Liouville equation and their numerical tests
The main purpose of this article is to show how structure reected in partial dierential equations can be preserved in a discrete world and reected in dierence schemes. Three dierent structureExpand
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Self-Dual Chern-Simons Solitons in Nonlinear σ-MODELS
A self-dual Chern-Simons system and its Lax pair are derived from the tangent space representation of a two-dimensional nonlinear σ-model, endowed with a gauge field. The related “matter” fieldExpand
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Comment on "Berry phase correction to electron density of states in solids".
A Comment on the Letter by Di Xiao, Junren Shi, and Qian Niu, Phys. Rev. Lett. 95, 137204 (2005). The authors of the Letter offer a Reply.
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Bilinearization of multidimensional topological magnets
A classical magnetic model with compact su(2) and non-compact su(1,1) spin phase space admitting the Hirota bilinear form is presented in an arbitrary number of space dimensions. The essential pointExpand
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