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Nonlinear Evolution Equations and Painlev Test by W.-H. Steeb,N. Euler Pdf
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 Painlev test, Painlev property and integrability. Both ordinary differential equations and partial differential equations are considered.
Nonlinear Evolution Equations and Painlevé Test by W-H Steeb,N Euler Pdf
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. Contents:IntroductionPainlevé Test and Ordinary Differential EquationsApplicationsZiglin's Theorems and NonintegrabilityGroup Theoretical Reduction of Partial Differential Equations and Painlevé TestPainlevé Property and Painlevé Test for Partial Differential EquationPainlevé Property and IntegrabilityHirota Technique and Painlevé TestDeformation of Painlevé Series under Symmetry ReductionIntegrable Field EquationsNonintegrable Field EquationsPainlevé Transcendents in Statistical Mechanics Readership: Mathematicians and physicists. Keywords:Nonlinear Differential Equations;Integrability;Painleve Test;Backlund Transformation;Soliton Equations;Symmetry SolutionsReview: “This excellent book is more than a survey on the Painlevé test, Painlevé property and integrability of both ordinary and partial differential equations; it also presents the recent progress in a rapidly growing field.” Mathematics Abstracts
Nonlinear Evolution Equations by Boling Guo,Fei Chen,Jing Shao,Ting Luo Pdf
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.
Nonlinear Evolution Equations and Dynamical Systems by Sandra Carillo,Orlando Ragnisco Pdf
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.
The Painlevé Handbook by Robert M. Conte,Micheline Musette Pdf
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.
Direct and Inverse Methods in Nonlinear Evolution Equations by Robert M. Conte,Franco Magri,Micheline Musette,Junkichi Satsuma,Pavel Winternitz Pdf
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 Dynamics by Muthusamy Lakshmanan,Shanmuganathan Rajaseekar Pdf
This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.
Nonlinear Evolution Operators and Semigroups by Nicolae H. Pavel Pdf
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.
Nonlinear Evolution Equations That Change Type by Barbara L. Keyfitz,Michael Shearer Pdf
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 by Wolfgang Arendt,Haim Brezis,Michel Pierre Pdf
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.
Nonlinear Evolution Equations And Dynamical Systems - Proceedings Of The 8th International Workshop (Needs '92) by Vladimir G Makhankov,O K Pashaev,I Puzynin Pdf
NEEDs '92 was held in Dubna, Russia in July 1992. This set of proceedings compiles the lectures and short contributions on the soliton theory and its applications presented during the conference. The topics covered included the most recent results on relevant problems of nonlinear evolution systems such as: Multidimensional Integrable Systems, Geometric and Algebraic Methods, Painleve Property, Lie-Backlund Symmetries, Spectral Methods, Solitons and Coherent Structures, Computational Methods, Quantum Field and String Theories, Nonlinear Optics and Hydrodynamics, Condensed Matter etc. The extent of coverage for these important topics makes this book useful, informative and insighful for the mathematics and theoretical physics community, both the senior researches and those just entering the field.
Nonlinear Evolution Equations by Boling Guo,Fei Chen,Jing Shao,Ting Luo Pdf
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.
Lectures on Nonlinear Evolution Equations by Reinhard Racke Pdf
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.
