Bäcklund and Darboux transformations : geometry and modern applications in soliton theory / / C. Rogers, W.K. Schief [[electronic resource]]

• Record Nr.: UNINA9910455604003321
• Autore: Rogers C.
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2002
• ISBN: 0-511-15790-8; 0-511-60635-4; 0-511-02054-6
• Descrizione fisica: 1 online resource (xvii, 413 pages) : digital, PDF file(s)
• Collana: Cambridge texts in applied mathematics ; ; 30
• Disciplina: 530.124
• Soggetti: Solitons; Bäcklund transformations; Darboux transformations
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Sommario/riassunto: This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-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 Bäcklund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics.