General high-order localized waves to the Bogoyavlenskii-Kadomtsev-Petviashvili equation

In this work, the Bogoyavlenskii-Kadomtsev-Petviashvili equation is investigated. By means of the Hirota bilinear system and Pfaffian, we demonstrate that the Bogoyavlenskii-Kadomtsev-Petviashvili equation has the Grammian determinant solution. On the basis of the Grammian determinant solution, we derive a class of exponentially localized wave solutions. It is shown that the exponentially localized wave solutions describe the fission and fusion phenomena between kink-type soliton and breather-type soliton. Further, general high-order localized waves consisting of kink-type, lump-type and breather-type solitons are derived by means of the general differential operators. These general high-order localized waves contain more plentiful dynamical behaviors. It is shown that the mixture of multiple wave solutions exhibit the fission and fusion phenomena among kink-type, lump-type and breather-type solitons. In addition, by choosing appropriate parameters, we construct general high-order lump-type soliton solutions. The results show that high-order lump-type solitons propagate with the variable speed on the curves. After collision, the lump-type solitons do not pass through each other, but rather are reflected back. The propagation paths of the lump-type solitons are changed completely.