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THE MINIMAL N=2 SUPEREXTENSION OF THE NLS EQUATION

S. Krivonos·A. Sorin
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Abstract

We show that the well known $N=1$ NLS equation possesses $N=2$ supersymmetry and thus it is actually the $N=2$ NLS equation. This supersymmetry is hidden in terms of the commonly used $N=1$ superfields but it becomes manifest after passing to the $N=2$ ones. In terms of the new defined variables the second Hamiltonian structure of the supersymmetric NLS equation coincides with the $N=2$ superconformal algebra and the $N=2$ NLS equation belongs to the $N=2$ $a=4$ KdV hierarchy. We propose the KP-like Lax operator in terms of the $N=2$ superfields which reproduces all the conserved currents for the corresponding hierarchy.

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S. Krivonos, A. Sorin. 1995-04-17. THE MINIMAL N=2 SUPEREXTENSION OF THE NLS EQUATION. https://doi.org/10.1016/0370-2693(95)00755-a

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