Abstract
The BC-KP hierarchy is an important sub-hierarchy of the KP hierarchy. In this paper, the BCr-KP hierarchy is investigated from three aspects. Firstly, we study the gauge transformation for the BCr-KP hierarchy. Different from the KP hierarchy, the gauge transformation must keep the constraint of the BCr-KP hierarchy. Secondly, we study the gauge transformation for the constrained BCr-KP hierarchy. In this case, the constraints of the Lax operator must be invariant under the gauge transformation. At last, the compatibility between the additional symmetry and the gauge transformation for the BCr-KP hierarchy is explored.
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