The N=2 Supersymmetric Heavenly Equation and Its Super-Hydrodynamical Reduction

Details The N=2 Supersymmetric Heavenly Equation and Its Super-Hydrodynamical Reduction The N=2 Supersymmetric Heavenly Equation and Its Super-Hydrodynamical Reduction

2003-02-27

arxiv.org/abs/nlin/0302061v1

J.Phys. A36 (2003) 9701-9710

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, LaTex

Scientific paper

10.1088/0305-4470/36/37/308

Manifest N=2 supersymmetric Toda systems are constructed from the $sl(n,n+1)$ superalgebras by taking into account their complex structure. In the $n\to \infty$ continuum limit an N=2 extension of the $(2+1)$-dimensional heavenly equation is obtained. The integrability is guaranteed by the existence of a supersymmetric Lax pair. We further analyze the properties of the $(1+1)$-dimensionally reduced system. Its bosonic sector is of hydrodynamical type. This is not the case for the whole supersymmetric system which, however, is super-hydrodynamical when properly expressed in terms of a supergeometry involving superfields and fermionic derivatives.

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