Backlund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory
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Overview
"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.Synopsis
Explores deep and fascinating connections between a ubiquitous class of physically important waves known as solitons.
Booknews
A textbook for a graduate or upper-level undergraduate course on the geometry of soliton theory, for students of applied mathematics or mathematical physics. Through the two transforms, it describes the many remarkable connections between results of classical differential geometry of the 19th and early 20th centuries, and recent soliton theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)