The Symbolic Computation Of Integrability Structures For Partial Differential Equations
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The Symbolic Computation Of Integrability Structures For Partial Differential Equations
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Author : Joseph Krasil'shchik
language : en
Publisher: Springer
Release Date : 2018-04-03
The Symbolic Computation Of Integrability Structures For Partial Differential Equations written by Joseph Krasil'shchik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-03 with Mathematics categories.
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.
Geometric Analysis Of Nonlinear Partial Differential Equations
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Author : Valentin Lychagin
language : en
Publisher: MDPI
Release Date : 2021-09-03
Geometric Analysis Of Nonlinear Partial Differential Equations written by Valentin Lychagin and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-03 with Mathematics categories.
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.
Continuous Symmetries And Integrability Of Discrete Equations
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Author : Decio Levi
language : en
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
Release Date : 2023-01-23
Continuous Symmetries And Integrability Of Discrete Equations written by Decio Levi and has been published by American Mathematical Society, Centre de Recherches Mathématiques this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-23 with Mathematics categories.
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.
The Diverse World Of Pdes
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Author : I. S. Krasil′shchik
language : en
Publisher: American Mathematical Society
Release Date : 2023-08-21
The Diverse World Of Pdes written by I. S. Krasil′shchik and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-21 with Mathematics categories.
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.
Analytical Properties Of Nonlinear Partial Differential Equations
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Author : Alexei Cheviakov
language : en
Publisher: Springer Nature
Release Date :
Analytical Properties Of Nonlinear Partial Differential Equations written by Alexei Cheviakov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Differential Equations Geometry Symmetries And Integrability
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Author : Boris Kruglikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-24
Differential Equations Geometry Symmetries And Integrability written by Boris Kruglikov 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 2009-07-24 with Mathematics categories.
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.
Nonlinear Systems Of Partial Differential Equations In Applied Mathematics Part 1
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Author : Basil Nicolaenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Nonlinear Systems Of Partial Differential Equations In Applied Mathematics Part 1 written by Basil Nicolaenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
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.
Nonlinear Systems And Their Remarkable Mathematical Structures
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Author : Norbert Euler
language : en
Publisher: CRC Press
Release Date : 2021-09-07
Nonlinear Systems And Their Remarkable Mathematical Structures written by Norbert Euler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-07 with Mathematics categories.
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.
Analytical Properties Of Nonlinear Partial Differential Equations
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Author : Alexei F. Cheviakov
language : en
Publisher:
Release Date : 2024
Analytical Properties Of Nonlinear Partial Differential Equations written by Alexei F. Cheviakov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Biomathematics categories.
Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will be of interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.
Discrete Integrable Systems
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Author : Basil Grammaticos
language : en
Publisher: Springer
Release Date : 2004-06-22
Discrete Integrable Systems written by Basil Grammaticos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-22 with Science categories.
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.