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The construction of special solutions to partial differential equations. (English) Zbl 0937.35501
Almost all the methods devised to date for constructing particular solutions to a partial differential equation can be viewed as manifestations of a single unifying method characterized by the appending of suitable ‘side conditions’ to the equation, and solving the resulting overdetermined system of partial differential equations. These side conditions can also be regarded as specifying the invariance of the particular solutions under some generalized groups of transformations.

MSC:
35A30Geometric theory for PDE, characteristics, transformations
22E99Lie groups
58J70Invariance and symmetry properties