Contact Geometry and Non-Linear Differential Equations
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BeschreibungShows novel and modern ways of solving differential equations using methods from contact and symplectic geometry.
InhaltsverzeichnisIntroduction; Part I. Symmetries and Integrals: 1. Distributions; 2. Ordinary differential equations; 3. Model differential equations and Lie superposition principle; Part II. Symplectic Algebra: 4. Linear algebra of symplectic vector spaces; 5. Exterior algebra on symplectic vector spaces; 6. A Symplectic classification of exterior 2-forms in dimension 4; 7. Symplectic classification of exterior 2-forms; 8. Classification of exterior 3-forms on a 6-dimensional symplectic space; Part III. Monge-Ampere Equations: 9. Symplectic manifolds; 10. Contact manifolds; 11. Monge-Ampere equations; 12. Symmetries and contact transformations of Monge-Ampere equations; 13. Conservation laws; 14. Monge-Ampere equations on 2-dimensional manifolds and geometric structures; 15. Systems of first order partial differential equations on 2-dimensional manifolds; Part IV. Applications: 16. Non-linear acoustics; 17. Non-linear thermal conductivity; 18. Meteorology applications; Part V. Classification of Monge-Ampere Equations: 19. Classification of symplectic MAEs on 2-dimensional manifolds; 20. Classification of symplectic MAEs on 2-dimensional manifolds; 21. Contact classification of MAEs on 2-dimensional manifolds; 22. Symplectic classification of MAEs on 3-dimensional manifolds.
PortraitAlexei Kushner is a Professor and Dean of the Department of Mathematics and Computer Science, and a Senior Researcher at the Russian Academy of Sciences. Valentin Lychagin is a Professor at the Institute of Mathematics and Statistics, Tromso University, and a Senior Researcher at the Institute for Theoretical and Experimental Physics in Moscow. Vladimir Rubtsov is a Professor at the Departement de Mathematiques, Angers University, and a Senior Researcher at the Institute for Theoretical and Experimental Physics in Moscow.
Pressestimmen'As a whole, (together with the many and very clearly worked out examples presented, which is one of the most important and highly appreciated merits of this book) the text is well written, very well organised and the exposition is very clear. So, I would allow myself to recommend it as a very useful stand-by introduction to the geometric view on linear and nonlinear differential equations.' Journal of Geometry and Symmetry in Physics
Untertitel: 'Encyclopedia of Mathematics an'. Sprache: Englisch.
Verlag: CAMBRIDGE UNIV PR
Erscheinungsdatum: Februar 2007
Seitenanzahl: 496 Seiten