Quantum Deformation Of MKP Hierarchy

The KP hierarchy and mKP hierarchy have attracted a lot of interest in the research of integrable systems.The paper aims to study some problems related the q-deformed mKP hierarchy and h-deformed mKP hierarchy.The first one is to present the Lax operator,Lax equation,wave function and additional symmetries of q-deformed mKP hierarchy.The second one is to construct the h-deformed mKP hierarchy.The third one is to study the recursion operator for the flow equations of the q-KP hierarchy under the n-reduction.It is a subject cross of quantum algebra and integrable system.The results not only can enrich the theory of the integrable system,but also provide some ties between integrable systems and quantum algebras.