dorsal/arxiv
View SchemaOn the Hamiltonian and Lagrangian structures of time-dependent reductions of evolutionary PDEs
| Authors | Monica Ugaglia |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9902006 |
| URL | https://arxiv.org/abs/solv-int/9902006 |
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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"abstract": "In this paper we study the reductions of evolutionary PDEs on the manifold of\nthe stationary points of time-dependent symmetries. In particular we describe\nhow the finite dimensional Hamiltonian structure of the reduced system is\nobtained from the Hamiltonian structure of the initial PDE and we construct the\ntime-dependent Hamiltonian function. We also present a very general Lagrangian\nformulation of the procedure of reduction. As an application we consider the\ncase of the Painleve\u0027 equations PI, PII, PIII, PVI and also certain higher\norder systems appeared in the theory of Frobenius manifolds.",
"arxiv_id": "solv-int/9902006",
"authors": [
"Monica Ugaglia"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "On the Hamiltonian and Lagrangian structures of time-dependent reductions of evolutionary PDEs",
"url": "https://arxiv.org/abs/solv-int/9902006"
},
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