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The geometry of the space of Cauchy data of nonlinear PDEs. (English) Zbl 1292.35011

The author develops a framework for an intrinsic study of Cauchy problems for general nonlinear partial differential equations. The main point is a generalisation of the construction of the first-order jet bundle via Grassmannians using flag bundles and the subsequent introduction of higher- and infinite-order bundles. These new bundles allow for a simultaneous treatment of solutions of differential equations and their Cauchy data. As an application, transversality conditions in the calculus of variations are studied.

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
14M15 Grassmannians, Schubert varieties, flag manifolds
35G25 Initial value problems for nonlinear higher-order PDEs
53B15 Other connections
58A20 Jets in global analysis
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References:

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