Details
| Original language | English |
|---|---|
| Article number | 012704 |
| Journal | Journal of mathematical physics |
| Volume | 50 |
| Issue number | 1 |
| Publication status | Published - 2009 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: Journal of mathematical physics, Vol. 50, No. 1, 012704, 2009.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the N=2 supersymmetric Camassa-Holm and Hunter-Saxton equations
AU - Lenells, J.
AU - Lechtenfeld, O.
N1 - Funding Information: J.L. acknowledges support from a Marie Curie Intra-European Fellowship. The work of O.L. is partially supported by DFG. Grant No. Le-838/9 Copyright: Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=59349092020&partnerID=8YFLogxK
U2 - 10.1063/1.3060125
DO - 10.1063/1.3060125
M3 - Article
AN - SCOPUS:59349092020
VL - 50
JO - Journal of mathematical physics
JF - Journal of mathematical physics
SN - 0022-2488
IS - 1
M1 - 012704
ER -