Various kinds of high-order solitons to the Bogoyavlenskii–Kadomtsev–Petviashvili equation

Abstract

In this work, the Bogoyavlenskii–Kadomtsev–Petviashvili equation which is used to describe the wave phenomenon in fluid mechanics is investigated. Based on the bilinear representation, perturbation method and Taylor expansion approach, we derive various kinds of high-order solitons including the N-kink soliton, n-order lump-type soliton and mixture solution of kink soliton and lump-type soliton. First, N-kink soliton solution is obtained by the bilinear representation and perturbation method. Second, by using the Taylor expansion approach for the 2n-kink soliton solution, n-order lump-type soliton is obtained. Third, by mean of the Taylor expansion approach for 2n-kink soliton solution in the N-kink soliton solution (1 < 2n < N), we construct the mixture solution consisting of (N − 2n)-kink soliton and n-order lump-type soliton. Interestingly, the collision between kink soliton and lump-type soliton can give rise to a high-order lump-type soliton.