Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory

Preface Acknowledgements General introduction and outline 1. Pseudospherical surfaces and the classical Backlund 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 Schrodinger 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 transfomations 7. Backlund transformation and Darboux matrix connections 8. Bianchi and Ernst systems: Backlund transformations and permutability theorems 9. Projective-minimal and isothermal-asymptotic surfaces A. The su(2)-so(3) isomorphism B. CC-ideals C. Biographies Bibliography.

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