On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations
Exactly Solvable and Integrable Systems
2009-03-12 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We consider N=2 supersymmetric extensions of the Camassa-Holm and Hunter-Saxton equations. We show that they admit geometric interpretations as Euler equations on the superconformal algebra of contact vector fields on the 1|2-dimensional supercircle. We use the bi-Hamiltonian formulation to derive Lax pairs. Moreover, we present some simple examples of explicit solutions. As a by-product of our analysis we obtain a description of the bounded traveling-wave solutions for the two-component Hunter-Saxton equation.
Cite
@article{arxiv.0809.0077,
title = {On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations},
author = {Jonatan Lenells and Olaf Lechtenfeld},
journal= {arXiv preprint arXiv:0809.0077},
year = {2009}
}
Comments
1+19 pages, 3 figures; v2: reference added; v3: more references added, published in LMP