Lecture Notes on Geometrical Aspects of Partial Differential Equations
- ISBN-10
- 9814513997
- ISBN-13
- 9789814513999
- Category
- Mathematics
- Pages
- 372
- Language
- English
- Published
- 1992-03-26
- Publisher
- World Scientific
- Author
- V V Zharinov
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:Introduction: Internal Geometry of PDE:Differential ManifoldsLie-Backlund MappingsLie-Backlund Fields and Infinitesimal SymmetriesCartan Forms, Currents and Conservation LawsC-Spectral Sequence. Further Properties of Conservation LawsTrivial Equations. The Formal Variational CalculusEvolution EquationsExternal Geometry of PDE:Differential SubmanifoldsNormal Projection. External Fields and FormsTrivial Ambient Differential ManifoldsThe Characteristic MappingThe Green's FormulaLow-Dimensional Conservation LawsBacklund CorrespondenceFurther Studies:Lagrangian FormalismHamiltonian EquationsExample: The Nambu's StringAppendix Readership: Graduate students and researchers in mathematical physics. keywords:Differential Manifolds;Lie-Bäcklund Mappings;Cartan Forms;Currents;Conservation Laws;Lagrangian Formation;Hamiltonian Equations
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