Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

Abstract

Abstract A (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynam-ics and plasma physics is hereby investigated. Via the Hirota method, bilinear Bäcklund transformation are obtained, along with two types of the analytic solutions. Kink-shaped soliton solutions are derived via the Hirota method. Breather solutions are derived via the extended homoclinic test approach and lump solutions are obtained from the breather solutions under a limiting procedure. We find that the shape and amplitude of the one-kink soliton keep unchanged during the propagation and the velocity of the one-kink soliton depends on all the coefficients in the equation. We graphically demonstrate that the interaction between the two-kink solitons is elastic, and analyse the solitons with the influence of the coefficients. We observe that the amplitudes and shapes of the breather and lump remain unchanged during the propagation, and graphically present the breathers and lumps with the influence of the coefficients in the equation.