Regular soliton solutions and singular soliton solutions for the modified Kadomtsev–Petviashvili equations

In this paper, we study the positive and the negative modified Kadomtsev–Petviashvili (mKP) equations. The mKP equations are completely integrable equations that admit N-soliton solutions and an infinite number of conserved densities. Multiple-soliton solutions are obtained for the positive model, whereas multiple–singular soliton solutions are established for the negative model. The analysis depends mainly on the Hirota’s bilinear method.