Solutions for the equations of the Kadomtsev-Petviashvili hierarchy are given in terms of Wronskian. The two-dimensional Toda lattice equation and the two-dimensional Toda molecule equation are investigated and their solutions are expressed in the form of two-directional Wronskian and double Wronskian. These solutions have common structure so that we can construct systems of these equations and their Wronskian solutions.
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Hirota et al. (1988) studied this question.