Continuous symmetries and integrability of discrete equations
著者
書誌事項
Continuous symmetries and integrability of discrete equations
（CRM monograph series, v. 38）
American Mathematical Society, c2022
- : hardcover
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注記
Includes bibliographical references (p. 435-471) and index
内容説明・目次
内容説明
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.
目次
Introduction
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 Index
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