In this article we present first an algorithm for calculating the determiningequations associated with so-called ``nonclassical method'' of symmetryreductions (a la Bluman and Cole) for systems of partial differentailequations. This algorithm requires significantly less computation time thanthat standardly used, and avoids many of the difficulties commonly encountered.The proof of correctness of the algorithm is a simple application of the theoryof Grobner bases. In the second part we demonstrate some algorithms which maybe used to analyse, and often to solve, the resulting systems of overdeterminednonlinear PDEs. We take as our principal example a generalised Boussinesqequation, which arises in shallow water theory. Although the equation appearsto be non-integrable, we obtain an exact ``two-soliton'' solution from anonclassical reduction.
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