A 2 - Component or N=2 Supersymmetric Camassa - Holm Equation

Abstract

The extended N=2 supersymmetric Camasa - Holm equation is presented. It is accomplishe by formulation the supersymmeytric version of the Fuchssteiner method. In this framework we use two supersymmetric recursion operators of the N=2, $\alpha =-2,4$ Korteweg - de Vries equation and constructed two different version of the supersymmetric Camassa - Holm equation. The bosonic sector of N=2, $\alpha =4$ supersymmetric Camassa - Holm equation contains two component generalization of this equation considered by Chen, Liu and Zhang and as a special case two component generalized Hunter - Saxton equation considered by Aratyn, Gomes and Zimerman, As a byproduct of our analysis we defined the N=2 supersymmetric Hunter - Saxton equation. The bihamiltonian structure is constructed for the supersymmetric N=2, $\alpha =4$ Camassa - Holm equation.

9 pages, Latex,corrected typos

References in corpus (3)

• A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions
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• Double Extended Cubic Peakon Equation
• On integrability of the Camassa-Holm equation and its invariants. A geometrical approach
• Euler Equations Related to the Generalized Neveu-Schwarz Algebra
• Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation
• The transformations between N=2 supersymmetric KdV and HD equations
• $G$-Strands and Peakon Collisions on $\mathrm{Diff}(\mathbb{R})$
• On the Cauchy problem of a two-component b-family equation
• Global existence and blow-up phenomena for a periodic 2-component Camassa-Holm equation with vorticity
• On the non-integrability of the Popowicz peakon system
• Superconformal Algebras and Supersymmetric Integrable Flows