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Titlebook: Hamiltonian Methods in the Theory of Solitons; Ludwig D. Faddeev,Leon A. Takhtajan Book 2007 Springer-Verlag Berlin Heidelberg 2007 Invers

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Fundamental Continuous Modelsnditions we shall analyze the mapping . from the initial data of the auxiliary linear problem to the transition coefficients and the discrete spectrum, and show how to solve the inverse problem, i. e. how to construct the mapping .. We shall see that these models allow an r-matrix approach, which wi
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Lie-Algebraic Approach to the Classification and Analysis of Integrable Modelsncipal entities of the inverse scattering method and its Hamiltonian interpretation were the auxiliary linear problem operator . = . − .(.) and the fundamental Poisson brackets for .(.) involving the r-matrix. Similar objects were introduced for lattice models. We will show that these notions have a
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https://doi.org/10.1007/978-3-662-03488-0 attracted a large number of research workers of different orientations ranging from algebraic geometry to applied hydrodynamics. Modern mathematical physics has witnessed the development of a vast new area of research devoted to this theory and called the inverse scattering method of solving nonlin
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The Physics of Structural Phase Transitions formulation. Then, motivated by these examples, we shall outline a general scheme for constructing integrable equations and their solutions based on the matrix Riemann problem. A detailed study of the most important models and the Hamiltonian interpretation of the general scheme will be presented i
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https://doi.org/10.1007/b138153nditions we shall analyze the mapping . from the initial data of the auxiliary linear problem to the transition coefficients and the discrete spectrum, and show how to solve the inverse problem, i. e. how to construct the mapping .. We shall see that these models allow an r-matrix approach, which wi
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