Olver, Peter J.; Rosenau, Philip Group-invariant solutions of differential equations. (English) Zbl 0621.35007 SIAM J. Appl. Math. 47, 263-278 (1987). The authors describe a general approach to group-invariant solutions of partial differential equations. They introduce the concept of a ”weak symmetry group” of a system of partial differential equations and show how, in principle, to construct group-invariant solutions for any group of transformations by reducing the number of variables in the system. But the paper also contains the result that every solution of a given system can be found using the reduction method with some weak symmetry group. The theoretical considerations are illustrated by a number of examples, including the heat equation, a nonlinear wave equation and a version of the Boussinesq equation. Reviewer: W.Watzlawek Cited in 4 ReviewsCited in 91 Documents MSC: 35A30 Geometric theory, characteristics, transformations in context of PDEs 35G20 Nonlinear higher-order PDEs Keywords:group-invariant solutions; weak symmetry group; group of transformations; heat equation; nonlinear wave equation; Boussinesq equation PDFBibTeX XMLCite \textit{P. J. Olver} and \textit{P. Rosenau}, SIAM J. Appl. Math. 47, 263--278 (1987; Zbl 0621.35007) Full Text: DOI