Backlund and Darboux Transformations

This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund 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 Backlund transformations of Painleve equations, to the dressing method and Backlund and Darboux transformations, and to the classical geometry of Backlund 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 Backlund and Darboux transformations.

ISBN 0821828037   Pages 436 ISBN13 9780821828038 (What's this?)   Volumes 001 Publisher American Mathematical Society   Weight (grammes) 772 Imprint American Mathematical Society   Published in Providence Format Paperback   Conference location Halifax Publication date 15 Oct 2001   Conference name International Proceedings Non-book description xx, 436 p. :   Series title CRM Proceedings & Lecture Notes Library of Congress QC174.26.W   Height (mm) 254 DEWEY 530.124   Width (mm) 178 DEWEY edition DC22   Academic level Professional / Scholarly

		Preface
		Albert Victor Backlund
		Gaston Darboux
		List of Participants
		Backlund Transformations of the Higher Order Painleve Equations by V. I. Gromak		3
		Dressing Method and Backlund and Darboux Transformations by D. Levi and O. Ragnisco		29
		The Classical Geometry of Backlund Transformations. Introduction to Applications in Soliton Theory by C. Rogers and W. K. Schief		53
		An Introduction to Integrable Difference and Differential Geometries: Affine Spheres, Their Natural Generalization and Discretization by W. K. Schief		69
		On Bianchi and Backlund Transformations of Two Dimensional Surfaces in Four Dimensional Euclidean Space by Yu. Aminov and A. Sym		91
		Group Invariant Solutions without Transversality and the Principle of Symmetric Criticality by Ian M. Anderson and Mark E. Fels and Charles G. Torre		95
		Multi-Component Matrix KP Hierarchies as Symmetry-Enhanced Scalar KP Hierarchies and Their Darboux-Backlund Solutions by H. Aratyn and E. Nissimov and S. Pacheva		109
		The Darboux-Backlund Transformation and Clifford Algebras by Jan L. Cieslinski		121
		On Discrete Painleve Equations as Backlund Transformations by P. A. Clarkson and E. L. Mansfield and H. N. Webster		129
		A Backlund Transformation for Timelike Surfaces of Constant Mean Curvature in R[superscript 1,2] by J. N. Clelland		141
		On Ribaucour Transformations by A. V. Corro and W. Ferreira and K. Tenenblat		151
		The Ribaucour Congruences of Spheres Within Lie Sphere Geometry by Adam Doliwa		159
		Backlund Transformations for the Reduced Maxwell-Bloch Equations by N. M. Ercolani		167
		Transformations of Quasilinear Systems Originating from the Projective Theory of Congruences by E. V. Ferapontov		179
		Backlund Links Between Different Analytic Descriptions of Constant Mean Curvature Surfaces by E. V. Ferapontov and A. M. Grundland		191
		More...

 Be the first to write a customer review