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A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy. (English) Zbl 0607.35075

The authors give an extension of the KP equation in a supersymmetric context. The usual program for completely integrable p.d.e’s is followed and solved: conservation laws, variational formalism, Gelfand-Dikii theory, involutivity. The paper is not self-contained; good references on supermanifolds and on KP are useful when reading this work. Such relevant papers are given in the references.
Reviewer: T.Ratiu

MSC:

35Q58 Other completely integrable PDE (MSC2000)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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References:

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[2] Chaichian, M., Kulish, P.: On the method of inverse scattering problem and B?cklund transformations for supersymmetric equations. Phys. Lett.78 B, 413 (1978)
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[4] d’Auria, R., Sciuto, S.: Group theoretical construction of two-dimensional supersymmetric models. Nucl. Phys. B171, 189 (1980)
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[10] Manin, Yu.: Algebraic aspects of differential equations. J. Sov. Math.11, 1 (1979) · Zbl 0419.35001
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