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Toda equation and its solutions in special functions. (English) Zbl 0948.39006

Summary: We show a unified technique how to derive exact solutions of the Toda equation written by the various special functions. The derivation method consists of combinations of i) the Hirota bilinear method of soliton theory, ii) recurrence relations of special functions and iii) elementary matrix calculations. The method is relatively easy and yet able to derive sufficiently wide class of special function solutions of the Toda equation.

MSC:

39A12 Discrete version of topics in analysis
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
33C90 Applications of hypergeometric functions
35Q51 Soliton equations
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