Backlund and Darboux Transformations

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 Bcklund and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory.