Lecture Notes On Geometrical Aspects Of Partial Differential Equations (Series On Soviet And East European Mathematics 9)

Lecture Notes On Geometrical Aspects Of Partial Differential Equations (Series On Soviet And East European Mathematics 9)

By: V. V. Zharinov (author)Hardback

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Description

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

Part 1: Infinite dimensional manifolds. Part 2 Differential manifolds and PDE: Cartan distributions and differential manifolds; Lie-Backlund mappings and symmetry groups; Lie-Backlund fields and infinitesimal symmetries; Cartan forms, currents and conservation laws; c-spectral sequence. Part 3 External geometry: Backlund correspondence; differential submanifolds and the normal projection; external fields and forms; Green's formula; characteristic mapping. Part 4 Examples: trivial equations; evolution equations; Cauchy-Kowalevsky equations; Hamiltonian equations; Euler-Lagrange equations; Noether theorem; the classical relativistic string. Part 5 Differential algebras and PDE: differential algebras; fields, forms and differential operators; resolutions of differential algebras; differential ideals; conservation laws of lower dimensions.

Product Details

  • ISBN13: 9789810207533
  • Format: Hardback
  • Number Of Pages: 372
  • ID: 9789810207533
  • ISBN10: 9810207530

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