A new extended dispersionless mKP hierarchy and hodograph solution

In this article, a new extended dispersionless mKP hierarchy (exdmKPH) is constructed to obtain two types of dispersionless mKP equations with self-consistent sources (dmKPSCS) and their associated conservation equations. Two reductions of this hierarchy are used to get two types of the corresponding dispersionless mKdV equations with self-consistent sources (dmKdVSCS). A hodograph solution for the first type of dmKdVSCS and Bäcklund transformation between the extended dispersionless KP hierarchy (exdKPH) and exdmKPH are also given.

► A new exdmKPH is constructed.
► The exdmKPH provides an effective way to find two types of dmKPSCS and their associated conservation equations.
► Two reductions of this hierarchy are also studied to get two types of dmKdVSCS.
► A hodograph solution for the first type of dmKdVSCS is obtained.
► Bäcklund transformation between exdKPH and exdmKPH is also given.