Lie-Bäcklund Transformations in Applications

Inbunden, Engelska, 1987

Del i serien Studies in Applied and Numerical Mathematics

813 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Beskrivning

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.

Produktinformation

Utgivningsdatum:1987-02-28
Mått:151 x 228 x 20 mm
Vikt:405 g
Format:Inbunden
Språk:Engelska
Serie:Studies in Applied and Numerical Mathematics
Antal sidor:134
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9780898711516

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Innehållsförteckning

IntroductionClassical FoundationsSurface-Transformations: Lie's First Questions, Finite-Order Generalization, Infinite-Order StructureTranformation of Families of Surfaces: Lie's Second Question, Bianchi-Lie Tranformation, Backlund TransformationsExamples of Backlund Transformations: Invariance TransformationsTransformations Relating Different Differential EquationsTangent Transformation Groups: Finite-Order Tangent Tranformations, Tangent Transformation Groups of Sophus Lie, Higher-Order Tangent Transformation Groups, Infinite-Order Tangent TransformationsLie-Backlund Tangent Transformation Groups, Lie-Backlund EquationsApplication to Differential Equations: Defining EquationsGroup Theoretical Nature of Conservation Laws, Lie via Lie-Backlund for Ordinary Differential Equations, Group Theoretical Equivalence of Quantum-Mechanical SystemsSome 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.