The Symbolic Computation of Integrability Structures for Partial Differential Equations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Symbolic Computation of Integrability Structures for Partial Differential Equations PDF full book. Access full book title The Symbolic Computation of Integrability Structures for Partial Differential Equations by Joseph Krasil'shchik. Download full books in PDF and EPUB format.
Author: Joseph Krasil'shchik
Publisher: Springer
ISBN: 3319716557
Category : Mathematics
Languages : en
Pages : 272
Get Book Here
Book Description
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: Joseph Krasil'shchik
Publisher: Springer
ISBN: 3319716557
Category : Mathematics
Languages : en
Pages : 272
Get Book Here
Book Description
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: Decio Levi
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
ISBN: 0821843540
Category : Mathematics
Languages : en
Pages : 520
Get Book Here
Book Description
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: Valentin Lychagin
Publisher: MDPI
ISBN: 303651046X
Category : Mathematics
Languages : en
Pages : 204
Get Book Here
Book Description
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: I. S. Krasil′shchik
Publisher: American Mathematical Society
ISBN: 1470471477
Category : Mathematics
Languages : en
Pages : 250
Get Book Here
Book Description
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
ISBN: 3031530748
Category :
Languages : en
Pages : 322
Get Book Here
Book Description
Author: Dongming Wang
Publisher: Springer Science & Business Media
ISBN: 3764374292
Category : Mathematics
Languages : en
Pages : 374
Get Book Here
Book Description
This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.
Author: Alain Goriely
Publisher: World Scientific
ISBN: 9814495921
Category : Science
Languages : en
Pages : 435
Get Book Here
Book Description
This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space.
Author: Norbert Euler
Publisher: CRC Press
ISBN: 1000423263
Category : Mathematics
Languages : en
Pages : 510
Get Book Here
Book Description
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:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 240
Get Book Here
Book Description
Author: Roman M. Cherniha
Publisher: MDPI
ISBN: 3038425265
Category : Mathematics
Languages : en
Pages : 427
Get Book Here
Book Description
This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry
