A new (gamma_n,sigma_k)-KP hierarchy with two new time series gamma_n and sigma_k, which consists of gamma_n-flow, sigma_k-flow and mixed gamma_n and sigma_k evolution equations of eigenfunctions, is proposed. Two reductions and constrained flows of (gamma_n,sigma_k)-KP hierarchy are studied. The dressing method is generalized to the (gamma_n,sigma_k)-KP hierarchy and some solutions are presented.
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