Cohomological Analysis of Partial Differential Equations and Secondary Calculus

ISBN-13: 9780821829226 / Angielski / Twarda / 2001

American Mathematical Society

Opis

This work is dedicated to fundamentals of a theory which is an analogue of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form given by D. Spencer and H. Goldschmidt and differential calculus over commutative algebras (Primary Calculus). The main result of this synthesis is secondary calculus on diffieties, new geometrical objects which are analogues of algebraic varieties in the context of (nonlinear) PDE's.