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Symmetries and integrability of difference equations

Author: D Levi
Publisher: Cambridge ; New York : Cambridge University Press, 2011.
Series: London Mathematical Society lecture note series, 381.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: D Levi
ISBN: 9780521136587 052113658X
OCLC Number: 707626621
Notes: 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.
Description: xviii, 341 pages : illustrations ; 23 cm.
Contents: Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals / V. Dorodnitsyn and R. Kozlov --
Painlevé equations: continuous, discrete and ultradiscrete / B. Grammaticos and A. Ramani --
Definitions and predictions of integrability for difference equations / J. Hietarinta --
Orthogonal polynomials, their recursions, and functional equations / M.E.H. Ismail --
Discrete Painlevé equations and orthogonal polynomials / A. Its --
Generalized Lie symmetries for difference equations / D. Levi and R.I. Yamilov --
Four lectures on discrete systems / S.P. Novikov --
Lectures on moving frames / P.J. Olver --
Lattices of compact semisimple Lie groups / J. Patera --
Lectures on discrete differential geometry / Yu. B Suris --
Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations / P. Winternitz.
Series Title: London Mathematical Society lecture note series, 381.
Responsibility: edited by Decio Levi [and others].
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Abstract:

A comprehensive introduction to the subject suitable for graduate students and researchers. This book is also an up-to-date survey of the current state of the art and thus will serve as a valuable  Read more...

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'The book can certainly be recommended to everyone interested in having a comprehensive overview of the current state of the art in this fascinating and important research field.' Frans Cantrijn, Read more...

 
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