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    LECTURE NOTES ON GEOMETRICAL ASPECTS OF PARTIAL DIFFERENTIAL EQUATIONS

    by V V Zharinov (Steklov Mathematical Institute)

    This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text.

     
    Contents:
    • Introduction: Internal Geometry of PDE:
      • Differential Manifolds
      • Lie-Backlund Mappings
      • Lie-Backlund Fields and Infinitesimal Symmetries
      • Cartan Forms, Currents and Conservation Laws
      • C-Spectral Sequence. Further Properties of Conservation Laws
      • Trivial Equations. The Formal Variational Calculus
      • Evolution Equations
    • External Geometry of PDE:
      • Differential Submanifolds
      • Normal Projection. External Fields and Forms
      • Trivial Ambient Differential Manifolds
      • The Characteristic Mapping
      • The Green's Formula
      • Low-Dimensional Conservation Laws
      • Backlund Correspondence
    • Further Studies:
      • Lagrangian Formalism
      • Hamiltonian Equations
      • Example: The Nambu's String
    • Appendix
     
    Readership: Graduate students and researchers in mathematical physics.
     
     
    372pp    Pub. date: Mar 1992  
    ISBN:   978-981-02-0753-3
    981-02-0753-0
       US$82 / £54

     


     

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    Updated on 14 February 2012