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 Backlund transformations; difference equations
and special functions; multidimensional consistency of integrable
lattice equations; associated linear problems (Lax pairs);
connections with Pade approximants and convergence algorithms;
singularities and geometry; Hirota's bilinear formalism for
lattices; intriguing properties of discrete Painleve 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 numerous exercises and the thorough list of
references will benefit upper-level undergraduate, and beginning
graduate students as well as researchers from other disciplines.
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