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OverviewThis 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. Full Product DetailsAuthor: Decio Levi , Pavel Winternitz , Ravil I. Yamilov , Centre de Recherches MathematiquesPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.479kg ISBN: 9780821843543ISBN 10: 0821843540 Pages: 496 Publication Date: 15 April 2023 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction Integrability and symmetries of nonlinear differential and difference equations in two independent variables Symmetries as integrability criteria Construction of lattice equations and their Lax pair Transformation groups for quad lattice equations Algebraic entropy of the nonautonomous Boll equations Translation from Russian of R. I. Yamilov, ''On the classification of discrete eqautions'', reference [841] No quad-graph equation can have a generalized symmetry given by the narita-Itoh-Bogoyavlensky equation Bibliography Subject IndexReviewsAuthor InformationDecio Levi, Roma Tre University, Rome, Italy, and INFN, Roma Tre Section, Rome, Italy. Pavel Winternitz, Universite de Montreal, QC, Canada. Ravil I. Yamilov, UFA Federal Research Center of the Russian Academy of Science, Russia. Tab Content 6Author Website:Countries AvailableAll regions |
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