The gauge transformations of the constrained q-deformed modified KP hierarchy and their relations with the additional symmetries

In this paper, two kinds of gauge transformations for the constrained q -deformed modified KP hierarchy and their relations with additional symmetries are discussed. The corresponding gauge transformations are required to keep both the Lax equation and the Lax operator, which can be obtained by choosing the special generating functions. Then the successive gauge transformations for the constrained q -modified KP hierarchy are investigated. Finally, we find that additional symmetry flows commute with the gauge transformation for the q -mKP hierarchy.