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

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. (c) 2005 Elsevier B.V. All rights reserved.