Modified Kadomtsev-Petviashvili Equation in (3+1) Dimensions: Multiple Front-Wave Solutions

A modified Kadomtsev Petviashvili (mKP) equation in (3+1) dimensions is presented. We reveal multiple front-waves solutions for this higher-dimensional developed equation, and multiple singular front-wave solutions as well. The constraints on the coefficients of the spatial variables, that assure the existence of these multiple front-wave solutions are investigated. We also show that this equation fails the Painleve test, and we conclude that it is not integrable in the sense of possessing the Painleve property, although it gives multiple front-wave solutions.