## The KW theorem for the SKP hierarchy.(English)Zbl 0966.37033

Summary: The supersymmetric Kadomtsev-Petviashvili (SKP) hierarchy was first introduced by Yu. I. Manin and A. O. Radul [Commun. Math. Phys. 98, 65-77 (1985; Zbl 0607.35075)]. In this letter, by the factorization $$L^n=L_nL_{n-1}\cdots L_1$$ with $$L_j=D+u_{j,0}+u_{j,-1}D^{-1}+u_{j,-2}D^{-2}+\cdots$$, $$j=1,2\cdots n$$, being the independent super-pseudodifferential operators, we construct the supersymmetric Miura transformation for the SKP hierarchy, which leads to decomposition of the second Poisson brackets based on $$L^n$$ to a direct sum. Each term in the sum contains the second brackets for $$L_j$$.

### MSC:

 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35Q58 Other completely integrable PDE (MSC2000) 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems

Zbl 0607.35075
Full Text:

### References:

 [1] Kupershmidt, B.A.; Wilson, G., Invent. math., 62, 403, (1981) [2] Dickey, L.A., Commun. math. phys., 87, 127, (1982) [3] L.A. Dickey, Soliton Equations and Hamiltonian Systems, Advanced Series in Math. Phys. vol. 12, Singapore, 1991. · Zbl 0753.35075 [4] Yi Cheng, Commun. Math. Phys. 171 (1995) 661. [5] Yi Cheng, Yi-shen Li, Phys. Lett. A 157 (1991) 22. [6] Yi Cheng, J. Math. Phys. 33 (1992) 3774. [7] Yi Cheng, Lett. Math. Phys. 33 (1995) 159; 36 (1996) 35. [8] Figueroa-O’Farrill, J.M.; Ramos, E., Phys. lett. B, 262, 265, (1991) [9] J.M. Figueroa-O’Farrill, E. Ramos, Commun. Math. Phys. 145 (1992) 43; Mod. Phys. Lett. A 10 (1995) 2767. [10] Jin-Chang Shaw, Ming-Hsien Tu, solv-int/9805002. [11] Manin, Yu.I.; Radul, A.O., Commun. math. phys., 98, 65, (1985) [12] Aratyn, H.; Nissimov, E.; Pacheva, S., Int. J. mod. phys. A, 12, 1265, (1997) [13] Aratyn, H.; Rasinariu, C., Phys. lett. B, 391, 99, (1997) [14] H. Aratyn, E. Nissimov, S. Pacheva, solv-int/9801021. [15] H. Aratyn, E. Nissimov, S. Pacheva, solv-int/9808004.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.