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Originalpublikation
Lenells, J.; Lechtenfeld, O.: On the N=2 supersymmetric Camassa-Holm and Hunter-Saxton equations. In: Journal of Mathematical Physics 50 (2009), Nr. 1, 012704. DOI: https://doi.org/10.1063/1.3060125
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.
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