Research On The Relevant Problems Of The Q-Deformed Constrained Modified KP Hierarchy

In recent years,the Lax operator,Lax equations,flow equations,additional symmetries,dressing operators,gauge transformations of the mKP hierarchy and the quantum-deformed mKP(q-mKP)hierarchy have been extensively studied.Based on the research of the constrained mKP hierarchy with the Kupershmidt-Kiso version,this paper extends to the constrained q-mKP(q-cmKP)hierarchy and the relevant problems of the q-cmKP hierarchy with M components.The main results of this paper as follows:(1)The sufficient and necessary conditions reducing the q-Wronskian solutions of q-mKP hierarchy to the M components q-cmKP hierarchy are given,then an example with M=1 is given.(2)The q-cmKP hierarchy is generated by the gauge transformations operator Tn+k.The sufficient and necessary conditions reducing the generalized q-Wronskian solutions of the q-mKP hierarchy to the M components q-cmKP hierarchy are given,then we give a corresponding example.When q?1,the results can be returned to the classical mKP hierarchy.