Order-independent method of characteristics. (English) Zbl 0689.35002

A method of characteristics is developed for any system of partial differential equations of any finite order that admits an isovector field V 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 when V 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.
Reviewer: D.G.B.Edelen


35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35F25 Initial value problems for nonlinear first-order PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
Full Text: DOI


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