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Direct And Inverse Methods In Nonlinear Evolution Equations

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Direct And Inverse Methods In Nonlinear Evolution Equations

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Author : Robert M. Conte
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-21

Direct And Inverse Methods In Nonlinear Evolution Equations written by Robert M. Conte and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-21 with Science categories.

Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables. The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.

Direct And Inverse Methods In Nonlinear Evolution Equations

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Author : Robert M. Conte
language : en
Publisher: Springer
Release Date : 2014-03-12

Direct And Inverse Methods In Nonlinear Evolution Equations written by Robert M. Conte and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Science categories.

The Painlev Handbook

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Author : Robert Conte
language : en
Publisher: Springer Nature
Release Date : 2020-11-07

The Painlev Handbook written by Robert Conte and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-07 with Science categories.

This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlevé test and shows how Painlevé analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schrödinger equation, the Korteweg-de Vries equation, Hénon-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic and quintic Ginzburg-Landau equations. Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic Ginzburg-Landau equations; a close look at physical problems involving the sixth Painlevé function; and an overview of new results since the book’s original publication with special focus on finite difference equations. The book features tutorials, appendices, and comprehensive references, and will appeal to graduate students and researchers in both mathematics and the physical sciences.

The Painlev Handbook

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Author : Robert M. Conte
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-23

The Painlev Handbook written by Robert M. Conte and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-23 with Science categories.

Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species). This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions. The examples chosen to illustrate these methods are mostly taken from physics. These include on the integrable side the nonlinear Schrödinger equation (continuous and discrete), the Korteweg-de Vries equation, the Hénon-Heiles Hamiltonians, on the nonintegrable side the complex Ginzburg-Landau equation (encountered in optical fibers, turbulence, etc), the Kuramoto-Sivashinsky equation (phase turbulence), the Kolmogorov-Petrovski-Piskunov equation (KPP, a reaction-diffusion model), the Lorenz model of atmospheric circulation and the Bianchi IX cosmological model. Written at a graduate level, the book contains tutorial text as well as detailed examples and the state of the art on some current research.

Nonlinear Evolution Equations And Dynamical Systems Proceedings Of The Workshop Needs 91

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Author : M Boiti
language : en
Publisher: World Scientific
Release Date : 1992-08-26

Nonlinear Evolution Equations And Dynamical Systems Proceedings Of The Workshop Needs 91 written by M Boiti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-26 with categories.

The Workshop NEEDS '91 brought together, from all over the world, scientists engaged in research on nonlinear systems, either their underlying mathematical properties or their physical applications. Accordingly, many talks were devoted to present methods of solution (like spectral transform) and to the investigation of structural (geometrical and/or algebraic) properties of (continuous and discrete) nonlinear evolution equations. Peculiar nonlinear systems, such as cellular automata, were also discussed. Applications to various fields of physics, namely, quantum field theory, fluid dynamics, general relativity and plasma physics were considered.

Classical And Quantum Nonlinear Integrable Systems

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Author : A Kundu
language : en
Publisher: CRC Press
Release Date : 2019-04-23

Classical And Quantum Nonlinear Integrable Systems written by A Kundu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-23 with Science categories.

Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories

B Cklund And Darboux Transformations

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Author : A. A. Coley
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-01-01

B Cklund And Darboux Transformations written by A. A. Coley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.

This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.

Integrable Hamiltonian Hierarchies

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Author : Vladimir Gerdjikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-02

Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-02 with Science categories.

This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.

Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics

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Author : Victor A. Galaktionov
language : en
Publisher: CRC Press
Release Date : 2006-11-02

Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics written by Victor A. Galaktionov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-02 with Mathematics categories.

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

Topics In Spatial Stochastic Processes

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Author : Vincenzo Capasso
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-21

Topics In Spatial Stochastic Processes written by Vincenzo Capasso and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-21 with Mathematics categories.

The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.

Direct And Inverse Methods In Nonlinear Evolution Equations

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