The applications of the gauge transformation for the BKP hierarchy |
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| Authors: | Jipeng Cheng Jingsong He |
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| Institution: | 1. Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR China;2. Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, PR China |
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| Abstract: | In this paper, we investigated four applications of the gauge transformation for the BKP hierarchy. Firstly, it is found that the orbit of the gauge transformation for the constrained BKP hierarchy defines a special (2+1)-dimensional Toda lattice equation structure. Then the tau function of the BKP hierarchy generated by the gauge transformation is shown to be the Pfaffian. And the higher Fay-like identities for the BKP hierarchy is also obtained through the gauge transformation. At last, the compatibility between the additional symmetry and the gauge transformation of the BKP hierarchy is proven. |
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| Keywords: | Gauge transformation The BKP hierarchy Pfaffian Fay-like identity Additional symmetry |
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