The Symbolic Computation Of Integrability Structures For Partial Differential Equations

Author : Joseph Krasil'shchik,Alexander Verbovetsky,Raffaele Vitolo
Publisher : Springer
Page : 263 pages
File Size : 49,9 Mb
Release : 2018-04-03
Category : Mathematics
ISBN : 9783319716558

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The Symbolic Computation of Integrability Structures for Partial Differential Equations by Joseph Krasil'shchik,Alexander Verbovetsky,Raffaele Vitolo Pdf

This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials. The mathematical part of the book is a new approach to integrability structures that allows to treat all of them in a unified way. The software is an official package of Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.

Author : Valentin Lychagin,Joseph Krasilshchik
Publisher : MDPI
Page : 204 pages
File Size : 42,9 Mb
Release : 2021-09-03
Category : Mathematics
ISBN : 9783036510460

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Geometric Analysis of Nonlinear Partial Differential Equations by Valentin Lychagin,Joseph Krasilshchik Pdf

This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.

Author : Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
Page : 520 pages
File Size : 46,8 Mb
Release : 2023-01-23
Category : Mathematics
ISBN : 9780821843543

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Continuous Symmetries and Integrability of Discrete Equations by Decio Levi,Pavel Winternitz,Ravil I. Yamilov Pdf

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.

Author : I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
Publisher : American Mathematical Society
Page : 250 pages
File Size : 47,6 Mb
Release : 2023-08-21
Category : Mathematics
ISBN : 9781470471477

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The Diverse World of PDEs by I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky Pdf

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry and high-order phase transitions, bi-Hamiltonian structures of KdV type, bundles of Weyl structures, Lax representations via twisted extensions of Lie algebras, energy functionals and normal forms of knots, and differential invariants of inviscid flows. The companion volume (Contemporary Mathematics, Volume 789) is devoted to Algebraic and Cohomological Aspects of PDEs.

Author : Alexei Cheviakov
Publisher : Springer Nature
Page : 322 pages
File Size : 41,6 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9783031530746

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Analytical Properties of Nonlinear Partial Differential Equations by Alexei Cheviakov Pdf

Author : Boris A. Kupershmidt
Publisher : World Scientific
Page : 402 pages
File Size : 54,7 Mb
Release : 1990
Category : Mathematics
ISBN : 9810203160

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Integrable and Superintegrable Systems by Boris A. Kupershmidt Pdf

Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.

Author : Boris Kruglikov,Valentin Lychagin,Eldar Straume
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 49,5 Mb
Release : 2009-07-24
Category : Mathematics
ISBN : 9783642008733

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Differential Equations - Geometry, Symmetries and Integrability by Boris Kruglikov,Valentin Lychagin,Eldar Straume Pdf

The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.

Author : Norbert Euler,Da-jun Zhang
Publisher : CRC Press
Page : 510 pages
File Size : 42,5 Mb
Release : 2021-09-07
Category : Mathematics
ISBN : 9781000423266

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Nonlinear Systems and Their Remarkable Mathematical Structures by Norbert Euler,Da-jun Zhang Pdf

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area . Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering Sciences. Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained.

Author : Basil Nicolaenko,Darryl D. Holm,James M. Hyman
Publisher : American Mathematical Soc.
Page : 494 pages
File Size : 41,9 Mb
Release : 1986
Category : Mathematics
ISBN : 0821811258

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Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 by Basil Nicolaenko,Darryl D. Holm,James M. Hyman Pdf

Focusing on the increased interplay of theoretical advances in nonlinear hyperbolic systems, completely integrable systems, and evolutionary systems of nonlinear partial differential equations, this title contains papers grouped in sections: integrable systems, hyperbolic systems, variational problems, evolutionary systems, and dispersive systems.

Author : Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 515 pages
File Size : 46,7 Mb
Release : 2014-09-01
Category : Computers
ISBN : 9783319105154

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Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf

This book constitutes the proceedings of the 16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014, held in Warsaw, Poland, in September 2014. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as Studies in polynomial algebra are represented by contributions devoted to factoring sparse bivariate polynomials using the priority queue, the construction of irreducible polynomials by using the Newton index, real polynomial root finding by means of matrix and polynomial iterations, application of the eigenvalue method with symmetry for solving polynomial systems arising in the vibration analysis of mechanical structures with symmetry properties, application of Gröbner systems for computing the (absolute) reduction number of polynomial ideals, the application of cylindrical algebraic decomposition for solving the quantifier elimination problems, certification of approximate roots of overdetermined and singular polynomial systems via the recovery of an exact rational univariate representation from approximate numerical data, new parallel algorithms for operations on univariate polynomials (multi-point evaluation, interpolation) based on subproduct tree techniques.

Author : A.S. Fokas,I.M. Gelfand
Publisher : Birkhäuser
Page : 0 pages
File Size : 52,6 Mb
Release : 2011-10-12
Category : Mathematics
ISBN : 1461275350

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Algebraic Aspects of Integrable Systems by A.S. Fokas,I.M. Gelfand Pdf

Irene Dorfman died in Moscow on April 6, 1994, shortly after seeing her beautiful book on Dirac structures [I]. The present volume contains a collection of papers aiming at celebrating her outstanding contributions to mathematics. Her most important discoveries are associated with the algebraic structures arising in the study of integrable equations. Most of the articles contained in this volume are in the same spirit. Irene, working as a student of Israel Gel'fand made the fundamental dis­ covery that integrability is closely related to the existence of bi-Hamiltonian structures [2], [3]. These structures were discovered independently, and al­ most simultaneously, by Magri [4] (see also [5]). Several papers in this book are based on this remarkable discovery. In particular Fokas, Olver, Rosenau construct large classes on integrable equations using bi-Hamiltonian struc­ tures, Fordy, Harris derive such structures by considering the restriction of isospectral flows to stationary manifolds and Fuchssteiner discusses similar structures in a rather abstract setting.

Author : Basil Grammaticos,Yvette Kosmann-Schwarzbach,Thamizharasi Tamizhmani
Publisher : Springer
Page : 472 pages
File Size : 53,8 Mb
Release : 2004-06-22
Category : Science
ISBN : 3540214259

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Discrete Integrable Systems by Basil Grammaticos,Yvette Kosmann-Schwarzbach,Thamizharasi Tamizhmani Pdf

This volume consists of a set of ten lectures conceived as both introduction and up-to-date survey on discrete integrable systems. It constitutes a companion book to "Integrability of Nonlinear Systems" (Springer-Verlag, 2004, LNP 638, ISBN 3-540-20630-2). Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

Author : Alexander Mikhailov
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 48,8 Mb
Release : 2008-11-25
Category : Science
ISBN : 9783540881100

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Integrability by Alexander Mikhailov Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 702 pages
File Size : 45,8 Mb
Release : 1995
Category : Aeronautics
ISBN : UIUC:30112048646605

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Scientific and Technical Aerospace Reports by Anonim Pdf

Author : A.M. Vinogradov
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400919488

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Symmetries of Partial Differential Equations by A.M. Vinogradov Pdf

2 The authors of these issues involve not only mathematicians, but also speci alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field. A. M. VINOGRADOV 3 Acta Applicandae Mathematicae 15: 3-21, 1989. © 1989 Kluwer Academic Publishers. Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results A. M. VINOORADOV Department of Mathematics, Moscow State University, 117234, Moscow, U. S. S. R. (Received: 22 August 1988) Abstract. The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed. AMS subject classifications (1980). 35A30, 58005, 58035, 58H05. Key words. Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions. o. Introduction In this paper we present the basic notions and results from the general theory of local symmetries and conservation laws of partial differential equations. More exactly, we will focus our attention on the main conceptual points as well as on the problem of how to find all higher symmetries and conservation laws for a given system of partial differential equations. Also, some general views and perspectives will be discussed.