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Bi-Hamiltonian nature of the equation u tx = u xy u y – u yy u x

Bi-Hamiltonian nature of the equation u tx = u xy u y – u yy u x Abstract We study non-linear integrable partial differential equations naturally arising as bi-Hamiltonian Euler equations related to the looped cotangent Virasoro algebra. This infinite-dimensional Lie algebra (constructed in (Ovsienko and Roger, Commun. Math. Phys. 273: 357–378, 2007)) is a generalization of the classical Virasoro algebra to the case of two space variables. Two main examples of integrable equations we obtain are quite well known. We show that the relation between these two equations is similar to that between the Korteweg–de Vries and Camassa–Holm equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

Bi-Hamiltonian nature of the equation u tx = u xy u y – u yy u x

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Publisher
de Gruyter
Copyright
Copyright © 2010 by the
ISSN
1867-1152
eISSN
1869-6090
DOI
10.1515/apam.2010.002
Publisher site
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Abstract

Abstract We study non-linear integrable partial differential equations naturally arising as bi-Hamiltonian Euler equations related to the looped cotangent Virasoro algebra. This infinite-dimensional Lie algebra (constructed in (Ovsienko and Roger, Commun. Math. Phys. 273: 357–378, 2007)) is a generalization of the classical Virasoro algebra to the case of two space variables. Two main examples of integrable equations we obtain are quite well known. We show that the relation between these two equations is similar to that between the Korteweg–de Vries and Camassa–Holm equations.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Mar 1, 2010

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