Homogeneous Hamiltonian operators and the theory of coverings

被引：9
|
作者：
Vergallo, Pierandrea [1 ]
Vitolo, Raffaele [1 ,2 ]
机构：
[1] Univ Salento, Dept Math & Phys E De Giorgi, Lecce, Italy
[2] Ist Nazl Fis Nucl, Sez Lecce, Lecce, Italy
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2021年 / 75卷
关键词：
Integrable systems; Hamiltonian PDE; Homogeneous Hamiltonian operator; Covering of PDEs; NONLOCAL SYMMETRIES; POISSON BRACKETS; DARBOUX THEOREM; SYSTEMS;
D O I：
10.1016/j.difgeo.2020.101713
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new method (by Kersten, Krasil'shchik and Verbovetsky), based on the theory of differential coverings, allows to relate a system of PDEs with a differential operator in such a way that the operator maps conserved quantities into symmetries of the system of PDEs. When applied to a quasilinear first-order system of PDEs and a Dubrovin-Novikov homogeneous Hamiltonian operator the method yields conditions on the operator and the system that have interesting differential and projective geometric interpretations. (c) 2020 Elsevier B.V. All rights reserved.
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页数：16
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