Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2004-04-08
J.Phys.A37:8031-8044,2004
Nonlinear Sciences
Exactly Solvable and Integrable Systems
21 pages
Scientific paper
10.1088/0256-307X/21/8/006
In this paper we construct the two component supersymmetric generalized Harry Dym equation which is integrable and study various properties of this model in the bosonic limit. In particular, in the bosonic limit we obtain a new integrable system which, under a hodograph transformation, reduces to a coupled three component system. We show how the Hamiltonian structure transforms under a hodograph transformation and study the properties of the model under a further reduction to a two component system. We find a third Hamiltonian structure for this system (which has been shown earlier to be a bi-Hamiltonian system) making this a genuinely tri-Hamiltonian system. The connection of this system to the modified dispersive water wave equation is clarified. We also study various properties in the dispersionless limit of our model.
Das Ashok
Popowicz Ziemowit
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