Some Geometric Evolution Equations Arising as Geodesic Equations on Groups of Diffeomorphisms Including the Hamiltonian Approach

Details Some Geometric Evolution Equations Arising as Geodesic Equations on Groups of Diffeomorphisms Including the Hamiltonian Approach Some Geometric Evolution Equations Arising as Geodesic Equations on Groups of Diffeomorphisms Including the Hamiltonian Approach

2006-09-03

arxiv.org/abs/math/0609077v1

Progress in Non Linear Differential Equations and Their Applications, Vol. 69. Birkhauser Verlag 2006. Pages 133-215

Mathematics

Analysis of PDEs

78 pages

Scientific paper

This is the extended version of a lecture course given at the University of Vienna in the spring term 2005. The main aim of this course was to understand the papers \cite{10} and \cite{11} and to give a complete account of existence and uniqueness of the solutions of the members of higher order of the hierarchies of Burgers' equation and the Korteweg-de Vries equation, including their derivation and all the necessary background, both on the circle and on the real line in the setting of rapidly decreasing functions. These are all geodesic equations of infinite dimensional regular Lie groups, namely the diffeomorphism group of the line or the circle and the corresponding Virasoro group.

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