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Lie-Backlund Transformations in Applications

Lie-Backlund Transformations in Applications

£43.99

Part of Studies in Applied and Numerical Mathematics

  • Date Published: June 1979
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Hardback
  • isbn: 9780898711516

£ 43.99
Hardback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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  • 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 Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity.

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    Product details

    • Date Published: June 1979
    • format: Hardback
    • isbn: 9780898711516
    • length: 134 pages
    • dimensions: 235 x 160 x 20 mm
    • weight: 0.401kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    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.

  • Authors

    Robert L. Anderson

    Nail H. Ibragimov

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