Titlebook: Solitons in Physics, Mathematics, and Nonlinear Optics; Peter J. Olver,David H. Sattinger Conference proceedings 1990 Springer-Verlag New

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Nonlinear Evolution Equations, Inverse Scattering and Cellular Automata,r which the Inverse Scattering Transform method applies. A discussion of this method of solution for certain prototype nonlinear evolution equations in continuous media in 1 + 1 and 2 + 1 dimensions is given. It also turns out that there are cellular automata which admit soliton solutions and have m

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Isospectral Flows: Their Hamiltonian Structures, Miura Maps and Master Symmetries,ally) (.+1) locally defined, compatible Hamiltonian structures which have a ., involving some operator ... The operators .. have a . for each specific spectral problem..Examples include spectral dependent versions of the Schrödinger operator and its super-extensions and of generalised Zakharov—Shaba

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Integrable Nonlinear Evolution Equations in the Description of Waves in the Shallow-Water Long-Waved subject just to the force of gravity. In the approximation of long waves at least three possible situations can arise:.In case (i) we get that the surface amplitude evolves according to the Kadomtsev-Petviashvili equation, in case (ii) to a cylindrical Korteweg-de Vries equation and in case (iii)

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,Bäcklund Transformations and the Painlevé Property,f the solution about its’ .. With reference to the Lax pair for a system, the Bácklund transformations are equivalent to transformations of linear systems developed by Darboux (Bäcklund-Darboux transformations)..For specific systems the Bäcklund-Darboux transformations lead to a reformulation of the

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