On the N = 2 supersymmetric Camassa–Holm and Hunter–Saxton equations

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 der...

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Bibliographic Details
Published in:Journal of mathematical physics 2009-01, Vol.50 (1), p.012704-012704-17
Main Authors: Lenells, J., Lechtenfeld, O.
Format: Article
Language:English
Subjects:
ALGEBRA
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Eulers equations
Exact sciences and technology
GEOMETRY
HAMILTONIANS
Mathematical methods in physics
MATHEMATICAL SOLUTIONS
Mathematics
Physics
Sciences and techniques of general use
SUPERSYMMETRY
Theoretical mathematics
Theoretical physics
TRAVELLING WAVES
TWO-DIMENSIONAL CALCULATIONS
VECTOR FIELDS
VECTORS
WAVE EQUATIONS
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Summary: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.
ISSN:0022-2488
1089-7658
1089-7658
DOI:10.1063/1.3060125