Lie-Baecklund Transformations in Applications
Will be published approx. on 28. February 1987
Book
Hardback
134 pages
978-0-89871-151-6 (ISBN)
Description
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 Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity.
More details
Series
Language
English
Place of publication
New York
United States
Target group
College/higher education
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 228 mm
Width: 152 mm
Thickness: 20 mm
Weight
399 gr
ISBN-13
978-0-89871-151-6 (9780898711516)
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Schweitzer Classification
Content
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.
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.