Robert L. Anderson and Nail H. Ibragimov
SIAM Studies in Applied Mathematics 1
This title presents an introduction to the classical treatment of Backlund and general surface transformations; and includes detailed and accessible techniques for constructing both groups of tranformations which will be of great value to the scientist and engineer in the analysis of mathematical models of physical phenomena. Classical and recent examples of Backlund transformations as applied to geometry, nonlinear optics, turbulence models, nonlinear waves and quantum mechanics are given. The authors discuss applications of LieBacklund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity.
Contents Introduction; Classical Foundations; SurfaceTransformations: Lie's First Questions, FiniteOrder Generalization, Infinite Order Structure; Tranformation of Families of Surfaces: Lie's Second Question, BianchiLie Tranformation, Backlund Transformations; Examples of Backlund Transformations: Invariance Transformations; Transformations Relating Different Differential Equations; Tangent Transformation Groups: FiniteOrder Tangent Tranformations, Tangent Transformation Groups of Sophus Lie, HigherOrder Tangent Transformation Groups, InfiniteOrder Tangent Transformations; LieBacklund Tangent Transformation Groups, LieBacklund Equations; Application to Differential Equations: Defining Equations; Group Theoretical Nature of Conservation Laws, Lie via LieBacklund for Ordinary Differential Equations, Group Theoretical Equivalence of QuantumMechanical Systems; Some Applications of Backlund Transformations: Nonlinear Optics, Solitons and the KdV Equation, Constants of the Motion and Conservation Laws, Weakly Dispersive ShallowWater Waves in Two Space Dimensions
1979 / x + 124 pages / Hardcover / ISBN13: 9780898711516 / ISBN10: 0898711517 / List Price $58.00 / SIAM Member Price $40.60 / Order Code AM01
