On the Hamiltonian and Lagrangian structures of time-dependent reductions of evolutionary PDEs

1999/02/05 by Monica Ugaglia, Ugaglia, Monica
Physics and Astronomy · #35Q53 #58F07 #70H33 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #msc:35Q53 #msc:58F07 #msc:70H33 #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9902006

46 pages, Tex, to be published in "Differential Geometry and Applications"

arxiv created 1999/02/05 · arxiv updated 2009/11/30

Abstract

In this paper we study the reductions of evolutionary PDEs on the manifold of the stationary points of time-dependent symmetries. In particular we describe how the finite dimensional Hamiltonian structure of the reduced system is obtained from the Hamiltonian structure of the initial PDE and we construct the time-dependent Hamiltonian function. We also present a very general Lagrangian formulation of the procedure of reduction. As an application we consider the case of the Painleve' equations PI, PII, PIII, PVI and also certain higher order systems appeared in the theory of Frobenius manifolds.

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