Description
Book SynopsisThis book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text.
Table of ContentsPart 1: Infinite dimensional manifolds. Part 2 Differential manifolds and PDE: Cartan distributions and differential manifolds; Lie-Backlund mappings and symmetry groups; Lie-Backlund fields and infinitesimal symmetries; Cartan forms, currents and conservation laws; c-spectral sequence. Part 3 External geometry: Backlund correspondence; differential submanifolds and the normal projection; external fields and forms; Green's formula; characteristic mapping. Part 4 Examples: trivial equations; evolution equations; Cauchy-Kowalevsky equations; Hamiltonian equations; Euler-Lagrange equations; Noether theorem; the classical relativistic string. Part 5 Differential algebras and PDE: differential algebras; fields, forms and differential operators; resolutions of differential algebras; differential ideals; conservation laws of lower dimensions.
