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arXiv · 0809.0077

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

Jonatan Lenells·Olaf Lechtenfeld
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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.

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Jonatan Lenells, Olaf Lechtenfeld. 2009-01-27. On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations. https://doi.org/10.1063/1.3060125

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