Manin, Yu. I.; Radul, A. O. A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy. (English) Zbl 0607.35075 Commun. Math. Phys. 98, No. 1, 65-77 (1985). 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 Cited in 5 ReviewsCited in 173 Documents 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.) Keywords:KP hierarchy; supermanifolds; Lax equations; variational calculus; complete integrability; KP equation; conservation laws; variational formalism; Gelfand-Dikii theory; involutivity PDFBibTeX XMLCite \textit{Yu. I. Manin} and \textit{A. O. Radul}, Commun. Math. Phys. 98, No. 1, 65--77 (1985; Zbl 0607.35075) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.