Lie-Baecklund Transformations in Applications

Introduction Classical Foundations Surface-Transformations: Lie's First Questions, Finite-Order Generalization, Infinite-Order Structure Tranformation of Families of Surfaces: Lie's Second Question, Bianchi-Lie Tranformation, Backlund Transformations Examples of Backlund Transformations: Invariance Transformations Transformations Relating Different Differential Equations Tangent Transformation Groups: Finite-Order Tangent Tranformations, Tangent Transformation Groups of Sophus Lie, Higher-Order Tangent Transformation Groups, Infinite-Order Tangent Transformations Lie-Backlund Tangent Transformation Groups, Lie-Backlund Equations Application to Differential Equations: Defining Equations Group Theoretical Nature of Conservation Laws, Lie via Lie-Backlund for Ordinary Differential Equations, Group Theoretical Equivalence of Quantum-Mechanical Systems Some Applications of Backlund Transformations: Nonlinear Optics, Solitons and the KdV Equation, Constants of the Motion and Conservation Laws, Weakly Dispersive Shallow-Water Waves in Two Space Dimensions.