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1 Paranjape, M. B Quantum Theory and Symmetries I11894 2021 eBook  
2 Levi, Decio Symmetries and Integrability of Difference Equations I10153 2017 eBook  
3 Conte, Robert M Direct and Inverse Methods in Nonlinear Evolution Equations I10544 2003 eBook  
4 Levi, Decio Painlev?? Transcendents I02541 1992 eBook  
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TitleQuantum Theory and Symmetries : Proceedings of the 11th International Symposium, Montreal, Canada
Author(s)Paranjape, M. B;MacKenzie, Richard;Thomova, Zora;Winternitz, Pavel;Witczak-Krempa, William
PublicationCham, Springer International Publishing, 2021.
DescriptionXVII, 670 p. 100 illus., 50 illus. in color : online resource
Abstract NoteThis volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montr??al, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions.
ISBN,Price9783030557775
Keyword(s)1. CONDENSED MATTER 2. CONDENSED MATTER PHYSICS 3. EBOOK 4. EBOOK - SPRINGER 5. Elementary particles (Physics) 6. Elementary Particles, Quantum Field Theory 7. Mathematical Methods in Physics 8. MATHEMATICAL PHYSICS 9. QUANTUM COMPUTERS 10. Quantum computing 11. QUANTUM FIELD THEORY
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TitleSymmetries and Integrability of Difference Equations : Lecture Notes of the Abecederian School of SIDE 12, Montreal 2016
Author(s)Levi, Decio;Rebelo, Rapha??l;Winternitz, Pavel
PublicationCham, Springer International Publishing, 2017.
DescriptionX, 435 p. 67 illus., 26 illus. in color : online resource
Abstract NoteThis book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers
ISBN,Price9783319566665
Keyword(s)1. ALGEBRA 2. Difference and Functional Equations 3. DIFFERENCE EQUATIONS 4. EBOOK 5. EBOOK - SPRINGER 6. Field theory (Physics) 7. Field Theory and Polynomials 8. FUNCTIONAL EQUATIONS 9. Numerical and Computational Physics, Simulation 10. PHYSICS
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TitleDirect and Inverse Methods in Nonlinear Evolution Equations : Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5???12, 1999
Author(s)Conte, Robert M;Magri, Franco;Musette, Micheline;Satsuma, Junkichi;Winternitz, Pavel;Greco, Antonio Maria
PublicationBerlin, Heidelberg, Springer Berlin Heidelberg, 2003.
DescriptionXI, 279 p : online resource
Abstract NoteMany 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 ?? la Painlev??, 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
ISBN,Price9783540398080
Keyword(s)1. COMPLEX SYSTEMS 2. DIFFERENTIAL GEOMETRY 3. DYNAMICAL SYSTEMS 4. EBOOK 5. EBOOK - SPRINGER 6. Mathematical Methods in Physics 7. PARTIAL DIFFERENTIAL EQUATIONS 8. PHYSICS 9. STATISTICAL PHYSICS 10. Statistical Physics and Dynamical Systems
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TitlePainlev?? Transcendents : Their Asymptotics and Physical Applications
Author(s)Levi, Decio;Winternitz, Pavel
PublicationNew York, NY, Springer US, 1992.
DescriptionXXVI, 446 p : online resource
Abstract NoteThe NATO Advanced Research Workshop "Painleve Transcendents, their Asymp?? totics and Physical Applications", held at the Alpine Inn in Sainte-Adele, near Montreal, September 2 -7, 1990, brought together a group of experts to discuss the topic and produce this volume. There were 41 participants from 14 countries and 27 lectures were presented, all included in this volume. The speakers presented reviews of topics to which they themselves have made important contributions and also re?? sults of new original research. The result is a volume which, though multiauthored, has the character of a monograph on a single topic. This is the theory of nonlinear ordinary differential equations, the solutions of which have no movable singularities, other than poles, and the extension of this theory to partial differential equations. For short we shall call such systems "equations with the Painleve property". The search for such equations was a very topical mathematical problem in the 19th century. Early work concentrated on first order differential equations. One of Painleve's important contributions in this field was to develop simple methods applicable to higher order equations. In particular these methods made possible a complete analysis of the equation ;; = f(y',y,x), where f is a rational function of y' and y, with coefficients that are analytic in x. The fundamental result due to Painleve (Acta Math
ISBN,Price9781489911582
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. MATHEMATICAL PHYSICS 4. Theoretical, Mathematical and Computational Physics
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