Nonlocal variations and local invariance of fields (Modern analytic and computational methods in science and mathematics)

Science & Math

Edelen, Dominic G. B.

Mathematics

American Elsevier Pub. Co.

Introduction to Linear Algebra for Science and Engineering [Jul 01, 1972] Edelen, Dominic G.B. and Kydoniefs, Anastasios D.

An introduction to linear algebra for science and engineering

Elsevier

Gauge theory and defects in solids

North-Holland

<p>The purpose of the book is to provide research workers in applied mathematics, physics, and engineering with practical geometric methods for solving systems of nonlinear partial differential equations. The first two chapters provide an introduction to the more or less classical results of Lie dealing with symmetries and similarity solutions. The results, however, are presented in the context of contact manifolds rather than the usual jet bundle formulation and provide a number of new conclusions. The remaining three chapters present essentially new methods of solution that are based on recent publications of the authors'. The text contains numerous fully worked examples so that the reader can fully appreciate the power and scope of the new methods. In effect, the problem of solving systems of nonlinear partial differential equations is reduced to the problem of solving families of autonomous ordinary differential equations. This allows the graphs of solutions of the system of partial differential equations to be realized as certain leaves of a foliation of an appropriately defined contact manifold. In fact, it is often possible to obtain families of solutions whose graphs foliate an open subset of the contact manifold. These ideas are extended in the final chapter by developing the theory of transformations that map a foliation of a contact manifold onto a foliation. This analysis gives rise to results of surprising depth and practical significance. In particular, an extended Hamilton-Jacobi method for solving systems of partial differential equations is obtained.</p>

Transformation Methods for Nonlinear Partial Differential Equations

Wang, Jian-Hua

World Scientific Pub Co Inc

See the best price to sell, buy, or rent books by Edelen, Dominic G. B.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Edelen, Dominic G. B.