E-raamat: Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics

Writing for those professionals and students seeking an introduction to the general theory of nonlinear evolution partial differential equations (PDEs) of different orders and types, Galaktionov (mathematics, U. of Bath) and Svirshchevskii (Keldysh Institute of Applied Mathematics) provide the first book-length systematic construction of exact solutions by way of linear invariant subspaces for nonlinear differential operators. They focus on new exact solutions on linear invariant subspaces for nonlinear operators and include applications from fluid mechanics, reaction-diffusion, wave propagation and thin-film theory, and supply a number of open-ended mathematical problems, including moving-mesh methods, blow-up aspects and discrete operators. They also include new examples of nonlinear models along with the standard, including nonlinear dispersion and Harry Dym equations, and offer exact solutions on invariant subspaces from some unharmonious lattices. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties.

This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders.

The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.