Symbolic Solutions for a Class of Partial Differential Equations

An algorithm to generate solutions for members of a class of completely integrable partial differential equations has been derived from a constructive proof of Frobeniusʹ Theorem. The algorithm is implemented as a procedure in the computer algebra system Maple. Because the implementation uses the facilities of Maple for solving sets of ordinary differential equations and for sets of nonlinear equations, and these facilities are limited, the problems that actually can be solved are restricted in size and complexity. Several examples, some derived from industrial practice, are presented to illustrate the use of the algorithm and to demonstrate the advantages and shortcomings of the implementation.