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A combination of dressing method and variation of constants as well as aformula for constructing the eigenfunction is used to solve the extended KPhierarchy, which is a hierarchy with one more series of time-flow and based onthe symmetry constaint of KP hierarchy. Similarly, extended mKP hierarchy isformulated and its zero curvature form, Lax representation and reductions arepresented. Via gauge transformation, it is easy to transform dressing solutionsof extended KP hierarchy to the solutions of extended mKP hierarchy. Wronskiansolutions of extended KP and extended mKP hierarchies are constructedexplicitly.

A Generalized Dressing Approach for Solving the Extended KP and the Extended mKP Hierarchy