Abstract
A systematic scheme to analyse the two-(space)-dimensional Toda lattice (2DTL) equation is proposed, making use of recurrence formulae similar to those of cylindrical functions. This scheme maintains a method to make linearize 2DTL equation and enables us to find various solutions, as well as ripplon-type solutions, by means of adjusting a set of coefficients of recurrence formulae. Several solutions are obtained by this method. A Bäcklund transformations is also found in this scheme to analyse the 2DTL equation. The compatibility condition to make linearize 2DTL equation is reduced to the original 2DTL equation itself.
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