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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:

[1] Saveliev, M.: Integrable supermanifolds and nonlinear systems. Preprint IHEP 84-20, Serpukhov (1984)
[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)
[3] Kupershmidt, B.: A super-Korteweg-de Vries equation: an integrable system. Preprint UTSI, Tullahoma (1984) · Zbl 0573.35079
[4] d’Auria, R., Sciuto, S.: Group theoretical construction of two-dimensional supersymmetric models. Nucl. Phys. B171, 189 (1980)
[5] Date, E., Kashiwara, M., Miwa, T.: Vertex operators and ?-functions. Transformation groups for soliton equations. II. Proc. Jpn. Acad. Sci.57 A, 387 (1981) · Zbl 0538.35066
[6] Date, E., Jimbo, M., Kashiwara, M., Miwa, T.: Operator approach to the Kadomtsev-Petviashvili equation. Transformation groups for soliton equations. III. J. Phys. Soc. Jpn.50, 3866 (1981) · Zbl 0571.35099
[7] Wess, J.: Supersymmetry-supergravity. In: Lecture Notes in Physics, Vol. 77. Berlin, Heidelberg, New York: Springer 1978 · Zbl 0516.53060
[8] Leites, D.: Introduction to the theory of supermanifolds. Russ. Math. Surv.35, 3 (1980) · Zbl 0462.58002
[9] Gelfand, I., Dikii, L.: Fractional powers of operators and hamiltonian systems. Funct. Analiz10, 13 (1976)
[10] Manin, Yu.: Algebraic aspects of differential equations. J. Sov. Math.11, 1 (1979) · Zbl 0419.35001
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