On Systems of Toda Type.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This report presents a group-theoretical interpretation of the structure of certain completely integrable Hamiltonian systems. These systems generalize the nonperiodic Toda Lattice system. Since all of them owe their special properties to the same group-theoretical mechanism, we call them systems of Toda type. This mechanism also provides a foundation for understanding many other completely integrable systems, including the Korteweg-de Vries equations, which will not be discussed here. We give an invariant definition of the class of systems of Toda type, and a method for explicit integration of all systems in this class in terms of rational combinations of linear exponential functions. Author
- Theoretical Mathematics