CRM Proceedings & Lecture Notes 2001; 436 pp; softcover Volume: 29 ISBN10: 0821828037 ISBN13: 9780821828038 List Price: US$138 Member Price: US$110.40 Order Code: CRMP/29
 This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Bäcklund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Bäcklund transformations of Painlevé equations, to the dressing method and Bäcklund and Darboux transformations, and to the classical geometry of Bäcklund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductory lectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Bäcklund and Darboux transformations. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students and research mathematicians interested in dynamical systems, ergodic theory, and partial differential equations. Table of Contents Introductory Lectures  V. I. Gromak  Bäcklund transformations of the higher order Painlevé equations
 D. Levi and O. Ragnisco  Dressing method and Bäcklund and Darboux transformations
 C. Rogers and W. K. Schief  The classical geometry of Bäcklund transformations. Introduction to applications in soliton theory
 W. K. Schief  An introduction to integrable difference and differential geometries: Affine spheres, their natural generalization and discretization
Original Contributions  Yu. Aminov and A. Sym  On Bianchi and Bäcklund transformations of two dimensional surfaces in four dimensional Euclidean space
 I. M. Anderson, M. E. Fels, and C. G. Torre  Group invariant solutions without transversality and the principle of symmetric criticality
 H. Aratyn, E. Nissimov, and S. Pacheva  Multicomponent matrix KP hierarchies as symmetryenhanced scalar KP hierarchies and their DarbouxBäcklund solutions
 J. L. Cieśliński  The DarbouxBäcklund transformation and Clifford algebras
 P. A. Clarkson, E. L. Mansfield, and H. N. Webster  On discrete Painlevé equations as Bäcklund transformations
 J. N. Clelland  A Bäcklund transformation for timelike surfaces of constant mean curvature in \(\mathbb R^{1,2}\)
 A. V. Corro, W. Ferreira, and K. Tenenblat  On Ribaucour transformations
 A. Doliwa  The Ribaucour congruences of spheres within Lie sphere geometry
 N. M. Ercolani  Bäcklund transformations for the reduced MaxwellBloch equations
 E. V. Ferapontov  Transformations of quasilinear systems originating from the projective theory of congruences
 E. V. Ferapontov and A. M. Grundland  Bäcklund links between different analytic descriptions of constant mean curvature surfaces
 F. Finkel  On the integrability of Weingarten surfaces
 F. Finkel and A. S. Fokas  A new immersion formula for surfaces on Lie algebras and integrable equations
 J. D. Finley III  Difficulties with the SDiff(2) Toda equation
 M. Havlíček, S. Pošta, and P. Winternitz  Superposition formulas based on nonprimitive group action
 R. H. Heredero, D. Levi, M. A. Rodríguez, and P. Winternitz  Symmetries of differential difference equations and Lie algebra contractions
 J. Hietarinta  Bäcklund transformations from the bilinear viewpoint
 L. Hlavatý  Towards the Lax formulation of SU(2) principal models with nonconstant metric
 C. A. Hoenselaers and S. Micciché  Transcendental solutions of the sineGordon equation
 T. Ioannidou, B. Piette, and W. J. Zakrzewski  Three dimensional skyrmions and harmonic maps
 B. G. Konopelchenko and G. Landolfi  Induced surfaces and their integrable deformations
 M. Kovalyov  Properties of a class of slowly decaying oscillatory solutions of KdV
 S. Lafortune, A. Ramani, B. Grammaticos, Y. Ohta, and K. M. Tamizhmani  Blending two discrete integrability criteria: Singularity confinement and algebraic entropy
 W.X. Ma and X. Geng  Bäcklund transformations of soliton systems from symmetry constraints
 P. Mathieu  Open problems for the super KdV equations
 R. Milson  Combinatorial aspects of the Darboux transformation
 M. Musette, R. Conte, and C. Verhoeven  Bäcklund transformation and nonlinear superposition formula of the KaupKupershmidt and Tzitzéica equations
 P. J. Olver, J. A. Sanders, and J. P. Wang  Classification of symmetryintegrable evolution equations
 E. G. Reyes  Integrability of evolution equations and pseudospherical surfaces
 C. Rogers and W. K. Schief  Infinitesimal Bäcklund transformations of \(K\)nets. The 2 + 1dimensional SinhGordon system
 W. K. Schief  Isothermic surfaces and the Calapso equation: The full Monty
 R. Schmid  Bäcklund transformations induced by symmetries. Application: Discrete mKdV
 H. Steudel  Darboux transformation for a spectral problem quadratic in the spectral parameter
 Z. Thomova and P. Winternitz  Separation of variables and Darboux transformations
 P. Winternitz  Bäcklund transformations as nonlinear ordinary differential, or difference equations with superposition formulas
