On a new generalization of dispersionless Kadomtsev–Petviashvili hierarchy and its reductions

Abstract

The dispersionless Kadomtsev–Petviashvili hierarchy is generalized by introducing two new time series γn and σk with two parameters ηn and λk. By this hierarchy, we obtain the first type, the second type as well as mixed type of dispersionless Kadomtsev–Petviashvili equation with self‐consistent sources and their related conservation equations. In addition, the reduction and constrained flow of this new hierarchy are studied. The first type, the second type and the mixed type of dispersionless Korteweg–de Vries equation with self‐consistent sources and of dispersionless Boussinesq equation with self‐consistent sources are obtained. Copyright © 2013 John Wiley & Sons, Ltd.