Continuous Symmetries and Integrability of Discrete Equations

Continuous Symmetries and Integrability of Discrete Equations
ISBN-10
0821843540
ISBN-13
9780821843543
Category
Mathematics
Pages
520
Language
English
Published
2023-01-23
Publisher
American Mathematical Society, Centre de Recherches Mathématiques
Authors
Pavel Winternitz, Decio Levi, Ravil I. Yamilov

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.

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