Nonautonomous solitons and Wronskian solutions for the (3+1)-dimensional variable-coefficient forced Kadomtsev–Petviashvili equation in the fluid or plasma

Abstract

Under investigation in this paper is a ( 3 + 1 )-dimensional variable-coefficient forced Kadomtsev–Petviashvili equation which can describe the nonautonomous solitons in such areas as fluids and plasmas. The first- and second-order nonautonomous solitons are constructed via the Hirota bilinear method. Propagation and interaction of the nonautonomous solitons are analyzed. Perturbation coefficient affects the amplitude of the nonautonomous soliton. The background where the nonautonomous soliton exists can be influenced by the external force coefficient. Breathers and resonant interaction, which are the special interaction structures for the second-order nonautonomous solitons, are also presented. Nonuniformity coefficient influences the period of the breather. For the resonant interaction, the two nonautonomous solitons merge into a single solitary wave and form three branches, the amplitudes of which are influenced by the perturbation coefficient. Solutions in terms of the Wronskian determinants are constructed and verified via the direct substitution into the bilinear form.