Abstract
A method of characteristics is developed for any system of partial differential equations of any finite order that admits an isovector fieldV and an initial data map satisfying a specific transversality condition. It is shown to agree with the classical method of characteristics for a nonlinear, first-order PDE and for quasilinear systems of first-order PDE with the same principal part. The method is also applicable to systems of nonlinear, first-order PDE and to systems of higher order, where it agrees with results obtained by similarity and group invariant methods. Implementation of the characteristic method is easier than classical group invariant methods because a complete, independent system of invariants of the flow generated by the isovector (group symmetry) does not have to be computed. General solutions are obtained only whenV is a Cauchy characteristic vector of the fundamental ideal; otherwise, any characteristic solution is shown to satisfy an explicit system of differential constraints. Explicit examples and comparisons with more classical methods are given.
Published Version
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