Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics
Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics

Author: W.I. Fushchich

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 456

ISBN-13: 9401731985

DOWNLOAD EBOOK

by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works [55-109, 176-189, 13-16, 7*-14*,23*, 24*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The authors wish to express their gratitude to Academician Yu.A. Mitropoi sky, and to Academician of Academy of Sciences of the Ukraine O.S. Parasyuk, for basic support and stimulation over the course of many years; to our cowork ers in the Department of Applied Studies, LA. Egorchenko, R.Z. Zhdanov, A.G. Nikitin, LV. Revenko, V.L Lagno, and I.M. Tsifra for assistance with the manuscript.

Nonlinear Dynamics
Nonlinear Dynamics

Author: H.G Solari

Publisher: Routledge

Published: 2019-01-22

Total Pages: 369

ISBN-13: 1351428306

DOWNLOAD EBOOK

Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and work

Nonlinear Symmetries and Nonlinear Equations
Nonlinear Symmetries and Nonlinear Equations

Author: G. Gaeta

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 275

ISBN-13: 9401110182

DOWNLOAD EBOOK

The study of (nonlinear) dift"erential equations was S. Lie's motivation when he created what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and algebra theory flourished and was applied to a number of dift"erent physical situations -up to the point that a lot, if not most, of current fun damental elementary particles physics is actually (physical interpretation of) group theory -the application of symmetry methods to dift"erential equations remained a sleeping beauty for many, many years. The main reason for this lies probably in a fact that is quite clear to any beginner in the field. Namely, the formidable comple:rity ofthe (algebraic, not numerical!) computations involved in Lie method. I think this does not account completely for this oblivion: in other fields of Physics very hard analytical computations have been worked through; anyway, one easily understands that systems of dOlens of coupled PDEs do not seem very attractive, nor a very practical computational tool.

Nonlinear Dynamical Systems Of Mathematical Physics: Spectral And Symplectic Integrability Analysis
Nonlinear Dynamical Systems Of Mathematical Physics: Spectral And Symplectic Integrability Analysis

Author: Denis Blackmore

Publisher: World Scientific

Published: 2011-03-04

Total Pages: 563

ISBN-13: 9814462713

DOWNLOAD EBOOK

This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field — including some innovations by the authors themselves — that have not appeared in any other book.The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained.This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.

Solitons in Mathematics and Physics
Solitons in Mathematics and Physics

Author: Alan C. Newell

Publisher: SIAM

Published: 1985-06-01

Total Pages: 259

ISBN-13: 0898711967

DOWNLOAD EBOOK

A discussion of the soliton, focusing on the properties that make it physically ubiquitous and the soliton equation mathematically miraculous.

Partial Differential Equations III
Partial Differential Equations III

Author: Michael E. Taylor

Publisher: Springer Science & Business Media

Published: 2010-11-02

Total Pages: 734

ISBN-13: 1441970495

DOWNLOAD EBOOK

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis

Nonlinear Partial Differential Equations for Scientists and Engineers
Nonlinear Partial Differential Equations for Scientists and Engineers

Author: Lokenath Debnath

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 602

ISBN-13: 1489928464

DOWNLOAD EBOOK

This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.