In the developing area of nonlinear mathematics, there are a large number of classes of nonlinear equations which have received attention. This collection of 11 articles addresses a number of physically motivated systems for which considerable theory is available, such as reaction-diffusion systems and elasticity. Theories that are available for wider classes of equations include discussions of Lie symmetries, improperly posed problems and integrable nonlinear equations. The main purpose of the book, however, is to address real situations. The range of applications presented to the reader is intended to help to make the developing studies of nonlinear mathematics more understandable.
Author(s): W.F. Ames and C. Rogers (Eds.)
Series: Mathematics in Science and Engineering 185
Publisher: Academic Press
Year: 1992
Language: English
Pages: iii-ix, 1-474
Tags: Математика;Математическая физика;
Content:
Edited by
Page iii
Copyright page
Page iv
Contributors
Pages vii-viii
Preface
Page ix
W.F. Ames, C. Rogers
Improperly Posed Problems for Nonlinear Partial Differential Equations Original Research Article
Pages 1-29
Karen A. Ames
Symmetry in Nonlinear Mechanics Original Research Article
Pages 31-78
W.F. Ames
Geometry of the Melnikov Vector Original Research Article
Pages 79-148
Shui-Nee Chow, Masahiro Yamashita
Nonlinear Waves Original Research Article
Pages 149-174
Andrea Donato
Integrable Nonlinear Equations Original Research Article
Pages 175-210
A.S. Fokas
Hamiltonian Structure and Integrability Original Research Article
Pages 211-256
Benno Fuchssteiner
Symmetric Chaos Original Research Article
Pages 257-315
Greg King, Ian Stewart
Bäcklund and Reciprocal Transformations: Gauge Connections Original Research Article
Pages 317-362
B.G. Konopelchenko, C. Rogers
Nonlinear Reaction-Diffusion Systems Original Research Article
Pages 363-398
R.H. Martin Jr., M. Pierre
Riccati-type Pseudopotentials and Their Applications Original Research Article
Pages 399-436
M.C. Nucci
Nonlinear Elasticity: Incremental Equations and Bifurcation Phenomena Original Research Article
Pages 437-468
R.W. Ogden
Index
Pages 469-474
