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Contact geometry and non-linear differential equations /
Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibil...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2007.
|
| Colección: | Encyclopedia of mathematics and its applications ;
volume 101. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Symmetries and integrals
- Distributions
- Ordinary differential equations
- Model differential equations and the lie superposition principle
- Symplectic algebra
- Linear algebra of symplectic vector spaces
- Exterior algebra on symplectic vector spaces
- A symplectic classification of exterior 2-forms in dimension 4
- Symplectic classification of exterior 2-forms
- Classification of exterior 3-forms on a six-dimensional symplectic space
- Monge-Ampère equations
- Symplectic manifolds
- Contact manifolds
- Monge-Ampère equations
- Symmetries and contact transformations of Monge-Ampère equations
- Conservation laws
- Monge-Ampère equations on two-dimensional manifolds and geometric structures
- Systems of first-order partial differential equations on two-dimensional manifolds
- Applications
- Non-linear acoustics
- Non-linear thermal conductivity
- Meteorology applications
- Classification of Monge-Ampère equations
- Classification of symplectic MAOs on two-dimensional manifolds
- Classification of symplectic MAEs on two-dimensional manifolds
- Contact classification of MAEs on two-dimensional manifolds
- Symplectic classification of MAEs on three-dimensional manifolds.