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Hamiltonian Methods in the Theory of Solitons pp 281–355Cite as

Basic Examples and Their General Properties

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Abstract

In this chapter we shall give a list of typical examples and establish their general properties: the zero curvature representation and the Hamiltonian 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 in the following chapters. The examples to be considered fall into two classes: dynamical systems generated by partial differential evolution equations (continuous models), and evolution systems of difference type (lattice models).

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  1. Steklov Mathematical Institute, Fontanka 27, 191011, Leningrad, USSR

    Ludwig D. Faddeev & Leon A. Takhtajan

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  1. Ludwig D. Faddeev
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Faddeev, L.D., Takhtajan, L.A. (2007). Basic Examples and Their General Properties. In: Hamiltonian Methods in the Theory of Solitons. Springer Series in Soviet Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69969-9_5

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