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

• General Introduction and Outline -- 1: Pseudospherical Surfaces and the Classical Bäcklund Transformation. The Bianchi System -- 2: The Motion of Curves and Surfaces. Soliton Connections -- 3: Tzitzeica Surfaces. Conjugate Nets and the Toda Lattice Scheme -- 4: Hasimoto Surfaces and the Nonlinear Schrödinger Equation. Geometry and Associated Soliton Equations -- 5: Isothermic Surfaces. The Calapso and Zoomeron Equations -- 6: General Aspects of Soliton Surfaces. Role of Gauge and Reciprocal Transformations -- 7: Bäcklund Transformation and Darboux Matrix Connections -- 8: Bianchi and Ernst Systems. Bäcklund Transformations and Permutability Theorems -- 9: Projective-Minimal and Isothermal-Asymptotic Surfaces. 

• 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. 

Ämnesord

Differential-och integralgeometri  (sao)

Projektiv geometri  (sao)

Solitons  (LCSH)

Bäcklund transformations  (LCSH)

Darboux transformations  (LCSH)

Genre

Electronic books.  (local)

Indexterm och SAB-rubrik

Tel Analytisk geometri

Tel Analytisk geometri

Klassifikation

QC174.26 (LCC)

530.124 (DDC)

Telf/DR (kssb/7)

Telf (kssb/7)