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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:
39A12Discrete version of topics in analysis
37K40Soliton theory, asymptotic behavior of solutions
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
33C90Applications of hypergeometric functions
35Q51Soliton-like equations