دانلود کتاب Discrete Systems and Integrability

This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations, difference equations and special functions, multidimensional consistency of integrable lattice equations, associated linear problems (Lax pairs), connections with Padé approximants and convergence algorithms, singularities and geometry, Hirota’s bilinear formalism for lattices, intriguing properties of discrete Painlevé equations and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the book’s numerous exercises and thorough list of references will benefit both upperlevel undergraduate and beginning graduate students as well as researchers from other disciplines.

JARMO HIETARINTA is Professor Emeritus of Theoretical Physics at the University
of Turku, Finland. His work has focused on the search for integrable systems of various
forms, including Hamiltonian mechanics, Hirota bilinear form, Yang–Baxter and tetrahedron
equations as well as lattice equations. He was instrumental in the setting up of the
nlin.SI category in arxiv.org and created the web pages for the SIDE (Symmetries and
Integrability of Difference Equations) conference series: http://side-conferences.net

NALINI JOSHI is Professor of Applied Mathematics at the University of Sydney. She
is best known for her work on the Painlevé equations and works at the leading edge of
international efforts to analyze discrete and continuous integrable systems in the geometric
setting of their initial-value spaces, constructed by resolving singularities in complex projective
space. She was elected as a Fellow of the Australian Academy of Science in 2008,
holds a Georgina Sweet Australian Laureate Fellowship and was awarded the special Hardy
Fellowship of the London Mathematical Society in 2015.

FRANK NIJHOFF is Professor of Mathematical Physics in the School of Mathematics
of the University of Leeds. His research focuses on nonlinear difference and differential
equations, symmetries and integrability of discrete systems, variational calculus, quantum
integrable systems and linear and nonlinear special functions. He was the principal
organizer of the 2009 six-month programme on Discrete Integrable Systems at the Isaac
Newton Institute, and a Royal Society Leverhulme Trust Senior Research Fellow in 2011.