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arXiv · 1803.08737

N=2 Supercomplexification of the Korteweg-de Vries, Sawada-Kotera and Kaup-Kupershmidt Equations

Ziemowit Popowicz
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Abstract

The supercomplexification is a special method of N=2 supersymmetrization of the integrable equations in which the bosonic sector could be reduced to the complex version of these equations. The N=2 supercomplex Korteweg de Vries, Sawada-Kotera and Kaup-Kupershmidt equations are defined and investigated. The common attribute of the supercomplex equations is appearance of the odd hamiltonian structures and superfermionic conservation laws. The odd bi-hamiltonian structure, Lax representation and superfermionic conserved currents for new N=2 supersymmetric Korteweg de Vries equation and for Sawada-Kotera, are given. The N=2 supercomplex Kaup-Kupershmidt equation is defined for which the odd bi-hamiltonian structure is presented with its superfermionic conserved currents.

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Ziemowit Popowicz. 2019-03-07. N=2 Supercomplexification of the Korteweg-de Vries, Sawada-Kotera and Kaup-Kupershmidt Equations. https://arxiv.org/abs/1803.08737

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