Euler-Poincare Formalism of Peakon Equations with Cubic Nonlinearity
Centre Interfacultaire Bernoulli, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland
- Corresponding Author:
- Guha P
Centre Interfacultaire Bernoulli
Ecole Polytechnique Federale
de Lausanne, SB CIB-GE Station 7
CH-1015 Lausanne, Switzerland
E-mail: [email protected]
Received date: May 11, 2015 Accepted date: July 20, 2015 Published date: July 29, 2015
Citation: Guha P (2015) Euler-Poincare Formalism of Peakon Equations with Cubic Nonlinearity. J Generalized Lie Theory Appl 9:225. doi:10.4172/1736-4337.1000225
Copyright: © 2015 Guha P. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
We present an Euler-Poincar´e (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.