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

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

2005-10-12

arxiv.org/abs/nlin/0510022v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages. to appear in Phys. Lett. A

Scientific paper

10.1016/j.physleta.2005.08.078

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.

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