Nonlinear Evolution Equations And Painleve Test
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Nonlinear Evolution Equations And Painleve Test
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Author : N Euler
language : en
Publisher: World Scientific
Release Date : 1988-10-01
Nonlinear Evolution Equations And Painleve Test written by N Euler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10-01 with Mathematics categories.
This book is an edited version of lectures given by the authors at a seminar at the Rand Afrikaans University. It gives a survey on the Painlevé test, Painlevé property and integrability. Both ordinary differential equations and partial differential equations are considered.
Nonlinear Evolution Equations And Dynamical Systems
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Author : Sandra Carillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Evolution Equations And Dynamical Systems written by Sandra Carillo 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 2012-12-06 with Science categories.
Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera- ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with Young-Baxter equations and Kac-Moody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography.
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.
Nonlinear Evolution Equations
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Author : Boling Guo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-11-05
Nonlinear Evolution Equations written by Boling Guo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Mathematics categories.
Nonlinear Evolution Equation presents state-of-the-art theories and results on nonlinear evolution equation, showing related mathematical methods and applications. The basic concepts and research methods of infinite dimensional dynamical systems are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and students in applied mathematics and physics.
Prolongation Structures Backlund Transformations And Painleve Analysis Of Nonlinear Evolution Equations
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Author :
language : en
Publisher:
Release Date : 2004
Prolongation Structures Backlund Transformations And Painleve Analysis Of Nonlinear Evolution Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
The Wahlquist-Estabrook prolongation technique and the Painleve analysis, used for testing the integrability of nonlinear evolution equations, are considered and applied both to the Drinfel'd-Sokolov system of equations, indeed known to be one of the coupled Korteweg-de Vries (KdV) systems, and Kersten-Krasil'shchik coupled KdV-mKdV equations. Some new Backlund transformations for the Drinfel'd-Sokolov system of equations are also found.
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
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Author : Songmu Zheng
language : en
Publisher: CRC Press
Release Date : 2004-07-08
Nonlinear Evolution Equations written by Songmu Zheng and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-08 with Mathematics categories.
Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator
Nonlinear Evolution Equations That Change Type
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Author : Barbara L. Keyfitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Evolution Equations That Change Type written by Barbara L. Keyfitz 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 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshop focussed on prob lems of ill-posedness and change of type which arise in modeling flows in porous materials, viscoelastic fluids and solids and phase changes. We thank the Coordinat ing Committee: James Glimm, Daniel Joseph, Barbara Lee Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the workshop organizers, Barbara Lee Keyfitz and Michael Shearer, for their efforts in bringing together many of the major figures in those research fields in which theories for nonlinear evolution equations that change type are being developed. A vner Friedman Willard Miller, J r. ix PREFACE During the winter and spring quarters of the 1988/89 IMA Program on Non linear Waves, the issue of change of type in nonlinear partial differential equations appeared frequently. Discussion began with the January 1989 workshop on Two Phase Waves in Fluidized Beds, Sedimentation and Granular Flow; some of the papers in the proceedings of that workshop present strategies designed to avoid the appearance of change of type in models for multiphase fluid flow.
Nonlinear Evolution Equations And Related Topics
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Author : Wolfgang Arendt
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Nonlinear Evolution Equations And Related Topics written by Wolfgang Arendt and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.
Lectures On Nonlinear Evolution Equations
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Author : Reinhard Racke
language : en
Publisher: Birkhäuser
Release Date : 2015-08-31
Lectures On Nonlinear Evolution Equations written by Reinhard Racke and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-31 with Mathematics categories.
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.