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EBOOK
Author Rogers, C.
Title Bäcklund and Darboux transformations : geometry and modern applications in soliton theory / C. Rogers, W.K. Schief.
Imprint Cambridge ; New York : Cambridge University Press, 2002.

Author Rogers, C.
Series Cambridge texts in applied mathematics
Cambridge texts in applied mathematics.
Subject Solitons.
Bäcklund transformations.
Darboux transformations.
Alt Name Schief, W. K. (Wolfgang Karl), 1964-
Description 1 online resource (xvii, 413 pages) : illustrations
Bibliography Note Includes bibliographical references and index.
Note Print version record.
Summary "This book describes the connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors explore the body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Backlund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Backlund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauss-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Backlund-Darboux transformations." "This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physicists."--Jacket.
Contents Machine generated contents note: 1. Pseudospherical Surfaces and the Classical Backlund Transformation. The Bianchi System -- 1.1. Gauss-Weingarten Equations for Hyperbolic Surfaces. Pseudospherical Surfaces. The Sine-Gordon Equation -- 1.2. Classical Backlund Transformation for the Sine-Gordon Equation -- 1.3. Bianchi's Permutability Theorem. Generation of Multi-Soliton Solutions -- 1.4. Pseudospherical Soliton Surfaces. Breathers -- 1.5. Parallel Surfaces. Induced Backlund Transformation for a Class of Weingarten Surfaces -- 1.6. Bianchi System. Its Auto-Backlund Transformation -- 2. Motion of Curves and Surfaces. Soliton Connections -- 2.1. Motions of Curves of Constant Torsion or Curvature. The Sine-Gordon Connection -- 2.2. 2 x 2 Linear Representation for the Sine-Gordon Equation -- 2.3. Motion of Pseudospherical Surfaces. A Weingarten System and Its Backlund Transformation -- 2.4.
ISBN 0511020546 (electronic bk.)
9780511020544 (electronic bk.)
9780521813310 (hb.)
052181331X (hb.)
9780521012881 (pb.)
0521012880 (pb.)
0511157908
9780511157905
9780511606359 (ebook)
0511606354 (ebook)
OCLC # 52740424
Additional Format Print version: Rogers, C. Bäcklund and Darboux transformations. Cambridge ; New York : Cambridge University Press, 2002 052181331X 0521012880 (DLC) 2001043453 (OCoLC)47805071



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