The construction of special solutions to partial differential equations

Abstract

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 group of transformations. © 1986.