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Zbl 0948.39006
Nakamura, Akira
Toda equation and its solutions in special functions. (English)
[J] J. Phys. Soc. Japan 65, No.6, 1589-1597 (1996). ISSN 0031-9015; ISSN 1347-4073/e

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 2000:: *39A12 Discrete version of topics in analysis
37K40 Soliton theory, asymptotic behavior of solutions
37K10 Completely integrable systems etc.
33C90 Appl. of hypergeometric functions
35Q51 Solitons

Keywords: exact solutions; Toda equation; Hirota bilinear method; soliton theory; recurrence relations; special functions

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