@MISC{Wolf00thesymbolic, author = {Thomas Wolf}, title = {The Symbolic Integration of Exact PDEs}, year = {2000} }

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Abstract

An algorithm is described which decides if a given polynomial differential expression \Delta of multivariate functions is exact, i.e. whether there exists a first integral P such that D x P = \Delta for any one x of a set of n variables and to provide the integral P . A generalization is given to allow integration in the case that the exactness is prevented by terms which contain only functions of less than n independent variables. 1 Motivation The common way to deal with problems that involve the solution of non-linear differential equations is to try different ansatze which are either geometrically motivated or just chosen to simplify computations. Typical examples are the investigation of infinitesimal symmetries, the search for classes of integrating factors and related first integrals/conservation laws or the search for a variational principle equivalent to a given system of equations. In all these cases over-determined systems of partial differential 1 equations (PDEs) have t...