Toda Equation and Its Solutions in Special Functions

We have shown a unified technique how to derive exact solutions of the Toda equation written by the various special functions. The derivation method consists of the combinations of i) Hirota bilinear method of the soliton theory, ii) recurrence relations of the 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.