On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations
نویسنده
چکیده
We consider N=2 supersymmetric extensions of the Camassa-Holm and HunterSaxton equations. We show that they admit geometric interpretations as Euler equations on the superconformal algebra of contact vector fields on the 1|2dimensional supercircle. We use the bi-Hamiltonian formulation to derive Lax pairs. Moreover, we present some simple examples of explicit solutions. As a byproduct of our analysis we obtain a description of the bounded traveling-wave solutions for the two-component Hunter-Saxton equation. PACS: 02.30.Ik, 11.30.Pb
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