On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations

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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

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Exactly Solvable and Integrable Systems, High Energy Physics - Theory, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/222934

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.0077
 http://arxiv.org/abs/0809.0077
 J.Math.Phys.50:012704,2009
 doi:10.1063/1.3060125

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arXiv