On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations
arXiv:0809.0077 · doi:10.1063/1.3060125
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.
1+19 pages, 3 figures; v2: reference added; v3: more references added, published in LMP