2005/09/30 by Ziemowit Popowicz
Physics and Astronomy · #nlin.SI
paper · pdf · doi:10.1016/j.physleta.2006.01.027
9 pages, Latex,corrected typos
arxiv created 2005/10/03 · arxiv updated 2009/12/01
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, α=-2,4 Korteweg - de Vries equation and constructed two different version of the supersymmetric Camassa - Holm equation. The bosonic sector of N=2, α=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, α=4 Camassa - Holm equation.