On the N=2 supersymmetric Camassa-Holm and Hunter-Saxton equations
2009 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 1, 012704Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2009. Vol. 50, no 1, 012704
Mathematics Physical Sciences
IdentifiersURN: urn:nbn:se:kth:diva-163824DOI: 10.1063/1.3060125ISI: 000262969800016ScopusID: 2-s2.0-59349092020OAI: oai:DiVA.org:kth-163824DiVA: diva2:802370
QC 201504272015-04-122015-04-122015-04-27Bibliographically approved