The geometry of the space of Cauchy data of nonlinear PDEs (Q2440512)

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.