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Toda equations and \(\sigma\)-functions of genera one and two. (English) Zbl 1039.37063
The author gives solutions of the continuous, discrete and ultradiscrete Toda equations. These solutions are derived from the addition formulae for elliptic and hyperelliptic \(\sigma\) functions.

MSC:
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
14H70 Relationships between algebraic curves and integrable systems
Keywords:
Toda equations
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