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arXiv · 1201.1612

The Recursion operators of the BKP hierarchy and the CKP Hierarchy

Maohua Li·Jipeng Cheng·Chuanzhong Li·Jingsong He
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Abstract

In this paper, under the constraints of the BKP(CKP) hierarchy, a crucial observation is that the odd dynamical variable $u_{2k+1}$ can be explicitly expressed by the even dynamical variable $u_{2k}$ in the Lax operator $L$ through a new operator $B$. Using operator $B$, the essential differences between the BKP hierarchy and the CKP hierarchy are given by the flow equations and the recursion operators under the $(2n+1)$-reduction. The formal formulas of the recursion operators for the BKP and CKP hierarchy under $(2n+1)$-reduction are given. To illustrate this method, the two recursion operators are constructed explicitly for the 3-reduction of the BKP and CKP hierarchies. The $t_7$ flows of $u_2$ are generated from $t_1$ flows by the above recursion operators, which are consistent with the corresponding flows generated by the flow equations under 3-reduction.

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Maohua Li, Jipeng Cheng, Chuanzhong Li, Jingsong He. 2012-01-08. The Recursion operators of the BKP hierarchy and the CKP Hierarchy. https://doi.org/10.1360/012013-42

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