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2015 Euler-Poincare Formalism of Peakon Equations with Cubic Nonlinearity
P Guha
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J. Gen. Lie Theory Appl. 9(1): 1-7 (2015). DOI: 10.4172/1736-4337.1000225


We present an Euler-Poincaré (EP) formulation of a new class of peakon equations with cubic nonlinearity, viz., Fokas-Qiao and V. Novikov equations, in two almost equivalent ways. The first method is connected to flows on the spaces of Hill’s and first order differential operator and the second method depends heavily on the flows on space of tensor densities. We give a comparative analysis of these two methods. We show that the Hamiltonian structures obtained by Qiao and Hone and Wang can be reproduced by EP formulation. We outline the construction for the 2+1-dimensional generalization of the peakon equations with cubic nonlinearity using the action of the loop extension of Vect(S1) on the space of tensor densities.


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P Guha. "Euler-Poincare Formalism of Peakon Equations with Cubic Nonlinearity." J. Gen. Lie Theory Appl. 9 (1) 1 - 7, 2015.


Published: 2015
First available in Project Euclid: 30 September 2015

zbMATH: 1345.35088
MathSciNet: MR3624047
Digital Object Identifier: 10.4172/1736-4337.1000225

Primary: 53A07 , 53B50

Keywords: 2+1-dimensional peakon equation , Bi-Hamiltonian , Fokas-Qiao equation , Novikov equation , Spaces of tensor densities

Rights: Copyright © 2015 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.9 • No. 1 • 2015
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