The constrained dispersionless mKP hierarchy and the dispersionless mKP hierarchy with self-consistent sources

Abstract We first show that the quasiclassical limit of the squared eigenfunction symmetry constraint of the Sato operator for the mKP hierarchy leads to a reduction of the Sato function for the dispersionless mKP hierarchy. The constrained dispersionless mKP hierarchy (cdmKPH) is obtained and it is shown that the ( 2 + 1 ) -dimensional dispersionless mKP hierarchy is decomposed to two ( 1 + 1 ) -dimensional hierarchies of hydrodynamical type. The dispersionless mKP hierarchy with self-consistent sources (dmKPHSCS) together with its associated conservation equations are also constructed. Some solutions of dmKPESCS are obtained by hodograph reduction method.