ALGORITHMS FOR THE NONCLASSICAL METHOD OF SYMMETRY REDUCTIONS

In this article the authors first present an algorithm for calculating the determining equations associated with so-called ''nonclassical me thod'' of symmetry reductions (a la Bluman and Cole) for systems of pa rtial differential equations. This algorithm requires significantly le ss computation time than that standardly used, and avoids many of the difficulties commonly encountered. The proof of correctness of the alg orithm is a simple application of the theory of Grobner bases. In the second part they demonstrate some algorithms which may be used to anal yse, and often to solve, the resulting systems of overdetermined nonli near PDEs. The authors take as their principal example a generalised B oussinesq equation, which arises in shallow water theory. Although the equation appears to be nonintegrable, the authors obtain an exact ''t wo-soliton'' solution from a nonclassical reduction.