The supercomplexification is a special method of N = 2 supersymmetrization of the integrable equations in which the bosonic sector can 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 one, are given.

中文翻译：

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N = 2 Korteweg-de Vries、Sawada-Kotera 和 Kaup-Kupershmidt 方程的超复杂化

超复杂化是可积方程的 N = 2 超对称化的一种特殊方法，其中玻色扇区可以简化为这些方程的复数形式。定义并研究了 N = 2 超复形 Korteweg-de Vries、Sawada-Kotera 和 Kaup-Kupershmidt 方程。超复方程的共同属性是奇哈密顿结构和超费米子守恒定律的出现。给出了新的 N = 2 超对称 Korteweg-de Vries 方程和 Sawada-Kotera 方程的奇数双哈密尔顿结构、Lax 表示和超费米子守恒电流。