Darboux transformation and nonautonomous solitons for a modified Kadomtsev–Petviashvili equation with variable coefficients

Abstract

We study a modified Kadomtsev–Petviashvili (mKP) equation with variable coefficients, which has important applications in fluid dynamics, ferromagnetics and plasma. The Lax pair, Hirota bilinear form and Darboux transformation (DT) are obtained through the two-singular manifold method. The N-soliton solution with Grammian type in a compact determinant representation is derived from the N-fold DT. A complete classification of the mKP-type solitons is given, namely, the bright and dark solitons, as well as resonant bright and dark solitons. Dynamics of the nonautonomous solitons with parabolic, periodic and kink shapes under different kinds of variable-coefficient oscillations are shown. Interactions between the nonautonomous two bright solitons and two resonant bright solitons are discussed through the asymptotic analysis method.