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Nonlinear Evolution Equations Integrability And Spectral Methods
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Book Synopsis Nonlinear Evolution Equations by : Antonio Degasperis
Download or read book Nonlinear Evolution Equations written by Antonio Degasperis and published by . This book was released on 1990 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Evolution Equations and Dynamical Systems by : Sandra Carillo
Download or read book Nonlinear Evolution Equations and Dynamical Systems written by Sandra Carillo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Evolution Equations And Dynamical Systems - Proceedings Of The 8th International Workshop (Needs '92) by : Vladimir G Makhankov
Download or read book Nonlinear Evolution Equations And Dynamical Systems - Proceedings Of The 8th International Workshop (Needs '92) written by Vladimir G Makhankov and published by World Scientific. This book was released on 1993-08-13 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Evolution Equations Solvable by the Spectral Transform by : F. Calogero
Download or read book Nonlinear Evolution Equations Solvable by the Spectral Transform written by F. Calogero and published by Pitman Publishing. This book was released on 1978 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains the text of the invited lectures presented at the International Symposium on "Nonlinear Evolution Equations Solvable by the Inverse Spectral Transform", that took place at the Accademia dei Lincei in Rome from June 15 through June 18, 1977. It introduces an important mathematical technique based on the spectral transform and relevant to the solution of nonlinear evolution equations. These texts will be of particular value to theoretical physicists (in plasma, nonlinear optics, hydrodynamics, solid state and elementary particles); applied mathematicians interested in nonlinear evolution equations; and pure mathematicians interested in algebraic and differential geometry.
Book Synopsis Algebraic and Spectral Methods for Nonlinear Wave Equations by : Naruyoshi Asano
Download or read book Algebraic and Spectral Methods for Nonlinear Wave Equations written by Naruyoshi Asano and published by Longman Scientific and Technical. This book was released on 1990 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Vladimir G. Makhankov Publisher :Springer Science & Business Media ISBN 13 :3642761720 Total Pages :256 pages Book Rating :4.6/5 (427 download)
Book Synopsis Nonlinear Evolution Equations and Dynamical Systems by : Vladimir G. Makhankov
Download or read book Nonlinear Evolution Equations and Dynamical Systems written by Vladimir G. Makhankov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the 6th International Workshop, 16-26 July 1990, Dubna, USSR
Book Synopsis Partially Integrable Evolution Equations in Physics by : R. Conte
Download or read book Partially Integrable Evolution Equations in Physics written by R. Conte and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the many physical phenomena ruled by partial differential equations, two extreme fields are currently overcrowded due to recent considerable developments: 1) the field of completely integrable equations, whose recent advances are the inverse spectral transform, the recursion operator, underlying Hamiltonian structures, Lax pairs, etc 2) the field of dynamical systems, often built as models of observed physical phenomena: turbulence, intermittency, Poincare sections, transition to chaos, etc. In between there is a very large region where systems are neither integrable nor nonintegrable, but partially integrable, and people working in the latter domain often know methods from either 1) or 2). Due to the growing interest in partially integrable systems, we decided to organize a meeting for physicists active or about to undertake research in this field, and we thought that an appropriate form would be a school. Indeed, some of the above mentioned methods are often adaptable outside their original domain and therefore worth to be taught in an interdisciplinary school. One of the main concerns was to keep a correct balance between physics and mathematics, and this is reflected in the list of courses.
Book Synopsis Nonlinear Evolution Equations And Dynamical Systems - Proceedings Of The Workshop (Needs '91) by : M Boiti
Download or read book Nonlinear Evolution Equations And Dynamical Systems - Proceedings Of The Workshop (Needs '91) written by M Boiti and published by World Scientific. This book was released on 1992-08-26 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :V. G. Makhanʹkov Publisher :World Scientific Publishing Company Incorporated ISBN 13 :9789810214487 Total Pages :486 pages Book Rating :4.2/5 (144 download)
Book Synopsis Nonlinear Evolution Equations & Dynamical Systems, NEEDS '92 by : V. G. Makhanʹkov
Download or read book Nonlinear Evolution Equations & Dynamical Systems, NEEDS '92 written by V. G. Makhanʹkov and published by World Scientific Publishing Company Incorporated. This book was released on 1993 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Evolution Equations and Painlev Test by : W.-H. Steeb
Download or read book Nonlinear Evolution Equations and Painlev Test written by W.-H. Steeb and published by World Scientific. This book was released on 1988 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Evolutions Equations Solvable by the Spectral Transform by : F. Calogero
Download or read book Nonlinear Evolutions Equations Solvable by the Spectral Transform written by F. Calogero and published by . This book was released on 1978 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Evolution Equations And Dynamical Systems, Proceedings Of The Icm2002 Satellite Conference by : Yi Cheng
Download or read book Nonlinear Evolution Equations And Dynamical Systems, Proceedings Of The Icm2002 Satellite Conference written by Yi Cheng and published by World Scientific. This book was released on 2003-10-14 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the papers presented at the ICM2002 Satellite Conference on Nonlinear Evolution Equations and Dynamical Systems. About 50 mathematicians and scientists attended the meeting — including E Witten (IAS), C Nappi (Princeton), K Khanin (Cambridge), D Phong (Columbia), d'Hoker (UCLA) and Peng Chiakuei (CAS). The book covers several fields, such as nonlinear evolution equations and integrable systems, infinite-dimensional algebra, conformal field theory and geometry.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)
Book Synopsis Lectures on Nonlinear Evolution Equations by : Reinhard Racke
Download or read book Lectures on Nonlinear Evolution Equations written by Reinhard Racke and published by Birkhäuser. This book was released on 2015-08-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Zeros of Polynomials and Solvable Nonlinear Evolution Equations by : Francesco Calogero
Download or read book Zeros of Polynomials and Solvable Nonlinear Evolution Equations written by Francesco Calogero and published by Cambridge University Press. This book was released on 2018-09-20 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reporting a novel breakthrough in the identification and investigation of solvable and integrable nonlinearly coupled evolution ordinary differential equations (ODEs) or partial differential equations (PDEs), this text includes practical examples throughout to illustrate the theoretical concepts. Beginning with systems of ODEs, including second-order ODEs of Newtonian type, it then discusses systems of PDEs, and systems evolving in discrete time. It reports a novel, differential algorithm which can be used to evaluate all the zeros of a generic polynomial of arbitrary degree: a remarkable development of a fundamental mathematical problem with a long history. The book will be of interest to applied mathematicians and mathematical physicists working in the area of integrable and solvable non-linear evolution equations; it can also be used as supplementary reading material for general applied mathematics or mathematical physics courses.
Book Synopsis Introduction to Multidimensional Integrable Equations by : B.G. Konopelchenko
Download or read book Introduction to Multidimensional Integrable Equations written by B.G. Konopelchenko and published by Springer. This book was released on 2013-06-12 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.
Book Synopsis Direct and Inverse Methods in Nonlinear Evolution Equations by : Robert M. Conte
Download or read book Direct and Inverse Methods in Nonlinear Evolution Equations written by Robert M. Conte and published by Springer Science & Business Media. This book was released on 2003-10-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Integrability by : Alexander Mikhailov
Download or read book Integrability written by Alexander Mikhailov and published by Springer Science & Business Media. This book was released on 2008-11-25 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of the book is to give a comprehensive account of the variety of approaches to such an important and complex concept as Integrability. Dev- oping mathematical models, physicists often raise the following questions: whether the model obtained is integrable or close in some sense to an integrable one and whether it can be studied in depth analytically. In this book we have tried to c- ate a mathematical framework to address these issues, and we give descriptions of methods and review results. In the Introduction we give a historical account of the birth and development of the theory of integrable equations, focusing on the main issue of the book – the concept of integrability itself. A universal de nition of Integrability is proving to be elusive despite more than 40 years of its development. Often such notions as “- act solvability” or “regular behaviour” of solutions are associated with integrable systems. Unfortunately these notions do not lead to any rigorous mathematical d- inition. A constructive approach could be based upon the study of hidden and rich algebraic or analytic structures associated with integrable equations. The requi- ment of existence of elements of these structures could, in principle, be taken as a de nition for integrability. It is astonishing that the nal result is not sensitive to the choice of the structure taken; eventually we arrive at the same pattern of eq- tions.