Mathematical Structures of Nonlinear Science

Mathematical Structures of Nonlinear Science

Author: Melvyn S. Berger

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 432

ISBN-13: 9400905793

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This is the first volume of a series of books that will describe current advances and past accompli shments of mathemat i ca 1 aspects of nonlinear sCience taken in the broadest contexts. This subject has been studied for hundreds of years, yet it is the topic in whi ch a number of outstandi ng di scoveri es have been made in the past two decades. Clearly, this trend will continue. In fact, we believe some of the great scientific problems in this area will be clarified and perhaps resolved. One of the reasons for this development is the emerging new mathematical ideas of nonlinear science. It is clear that by looking at the mathematical structures themselves that underlie experiment and observation that new vistas of conceptual thinking lie at the foundation of the unexplored area in this field. To speak of specific examples, one notes that the whole area of bifurcation was rarely talked about in the early parts of this century, even though it was discussed mathematically by Poi ncare at the end of the ni neteenth century. I n another di rect ion, turbulence has been a key observation in fluid dynamics, yet it was only recently, in the past decade, that simple computer studies brought to light simple dynamical models in which chaotic dynamics, hopefully closely related to turbulence, can be observed.


Nonlinear Systems and Their Remarkable Mathematical Structures

Nonlinear Systems and Their Remarkable Mathematical Structures

Author: Taylor & Francis Group

Publisher: CRC Press

Published: 2020-12-18

Total Pages: 582

ISBN-13: 9780367732431

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Nonlinear Systems and Their Remarkable Mathematical Structures aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Written by experts, each chapter is self-contained and aims to clearly illustrate some of the mathematical theories of nonlinear systems. The book should be suitable for some graduate and postgraduate students in mathematics, the natural sciences, and engineering sciences, as well as for researchers (both pure and applied) interested in nonlinear systems. The common theme throughout the book is on solvable and integrable nonlinear systems of equations and methods/theories that can be applied to analyze those systems. Some applications are also discussed. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-expert in this field Written to be accessible to some graduate and postgraduate students in mathematics and applied mathematics Serves as a literature source in nonlinear systems


Nonlinear Science

Nonlinear Science

Author: Alwyn Scott

Publisher: Oxford University Press, USA

Published: 1999

Total Pages: 504

ISBN-13:

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Problems and summaries after each chapter


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

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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.


Waves and Structures in Nonlinear Nondispersive Media

Waves and Structures in Nonlinear Nondispersive Media

Author: Sergey Nikolaevich Gurbatov

Publisher: Springer Science & Business Media

Published: 2012-03-23

Total Pages: 477

ISBN-13: 3642236170

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"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is the Full member of Russian Academy of Sciences, the head of Department at Moscow University and Professor at BTH (Sweden). Dr. Saichev A.I. is the Professor at the Faculty of Radiophysics of Nizhny Novgorod State University, Professor of ETH Zürich.


Encyclopedia of Nonlinear Science

Encyclopedia of Nonlinear Science

Author: Alwyn Scott

Publisher: Routledge

Published: 2006-05-17

Total Pages: 1107

ISBN-13: 1135455589

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In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.


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

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


Nonlinear Structural Mechanics

Nonlinear Structural Mechanics

Author: Walter Lacarbonara

Publisher: Springer Science & Business Media

Published: 2013-01-09

Total Pages: 812

ISBN-13: 1441912762

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This book reviews the theoretical framework of nonlinear mechanics, covering computational methods, applications, parametric investigations of nonlinear phenomena and mechanical interpretation towards design. Builds skills via increasing levels of complexity.


Introduction to the Mathematical Physics of Nonlinear Waves

Introduction to the Mathematical Physics of Nonlinear Waves

Author: Minoru Fujimoto

Publisher: Morgan & Claypool Publishers

Published: 2014-03-01

Total Pages: 217

ISBN-13: 1627052771

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Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environment


Nonlinear Dynamics

Nonlinear Dynamics

Author: H.G Solari

Publisher: Routledge

Published: 2019-01-22

Total Pages: 369

ISBN-13: 1351428306

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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