Mathematical Sciences: Non-classical symmetries of differential equations

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To develop new methods beyond the classical method of group- invariant solutions for finding explicit solutions to systems of partial differential equations, and apply them to physically important systems and boundary value problems. The methods to be investigated will include non-classical symmetries, partially invariant solutions, partial symmetries, the Clarkson-Kruskal direct method, and weak symmetry groups. These methods can all be subsumed through the general theory of "side conditions" and overdetermined systems of partial differential equations. The emphasis of this project will be on the determination of new exact solutions to physically important boundary value, Cauchy and mixed problems for partial differential equations.