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In this paper, we investigated four applications of the gauge transformationfor the BKP hierarchy. Firstly, it is found that the orbit of the gaugetransformation for the constrained BKP hierarchy defines a special $(2+1)$-dimensional Toda lattice equation structure. Then the tau function of theBKP hierarchy generated by the gauge transformation is showed to be thePfaffian. And the higher Fay-like identities for the BKP hierarchy is alsoobtained through the gauge transformation. At last, the compatibility betweenthe additional symmetry and the gauge transformation of the BKP hierarchy isproved.

The applications of the gauge transformation for the BKP hierarchy