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- 题名/责任者:
- Symmetries and integrability of difference equations / edited by Decio Levi ... [et al.].
- 出版发行项:
- Cambridge ; New York : Cambridge University Press, 2011.
- ISBN:
- 9780521136587 (pbk.)
- ISBN:
- 052113658X (pbk.)
- 载体形态项:
- xviii, 341 p. : ill. ; 23 cm.
- 丛编统一题名:
- London Mathematical Society lecture note series ; 381.
- 附加个人名称:
- Levi, D. (Decio)
- 论题主题:
- Difference equations.
- 论题主题:
- Symmetry (Mathematics)
- 论题主题:
- Integrals.
- 中图法分类号:
- O175-53
- 一般附注:
- Machine generated contents note: 1. Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals V. Dorodnitsyn and R. Kozlov; 2. Painleve; equations: continuous, discrete and ultradiscrete B. Grammaticos and A. Ramani; 3. Definitions and predictions of integrability for difference equations J. Hietarinta; 4. Orthogonal polynomials, their recursions, and functional equations M. E. H. Ismail; 5. Discrete Painleve; equations and orthogonal polynomials A. Its; 6. Generalized Lie symmetries for difference equations D. Levi and R. I. Yamilov; 7. Four lectures on discrete systems S. P. Novikov; 8. Lectures on moving frames P. J. Olver; 9. Lattices of compact semisimple Lie groups J. Patera; 10. Lectures on discrete differential geometry Yu. B Suris; 11. Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations P. Winternitz.
- 书目附注:
- Includes bibliographical references.
- 摘要附注:
- "Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference"--Provided by publisher.
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