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Zbl 0621.35007
Olver, Peter J.; Rosenau, Philip
Group-invariant solutions of differential equations. (English)
[J] SIAM J. Appl. Math. 47, 263-278 (1987). ISSN 0036-1399; ISSN 1095-712X/e

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.
[W.Watzlawek]

MSC 2000:: *35A30 Geometric theory for PDE, transformations
35G20 General theory of nonlinear higher-order PDE

Keywords: group-invariant solutions; weak symmetry group; group of transformations; heat equation; nonlinear wave equation; Boussinesq equation

Cited in: Zbl 1009.35004 Zbl 0949.35062 Zbl 0831.35007

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