Variety interaction between k-lump and k-kink solutions for the (3+1)-D Burger system by bilinear analysis

In this paper, we investigate the (3+1)-dimensional Burger system which is employed in soliton theory and generated by considering the Hirota bilinear equation. We conclude some novel analytical solutions, including 2-lump-type, interaction between 2-lump and one kink, two lump and two kink of type I, two lump and two kink of type II, two lump and one periodic, two lump and kink-periodic, and two lump and periodic–periodic wave solutions for the considered system by symbolic estimations. The main ingredients for this scheme are to recover the Hirota trilinear forms and their generalized equivalences. Then we apply explicit numerical methods, most of which are recently introduced by many scholars, to reproduce the analytical solutions. The test results show that the best algorithms, especially the Hirota bilinear, are very efficient and severely outperform the other methods. •In this paper, we study the (3+1)-dimensional Burger system by using the Hirota bilinear operators.•We retrieve 2-lump-type wave, interaction between 2-lump and one kink wave solutions.•The required conditions of the analyticity and positivity of the solutions are considered.•The main ingredients for this scheme are to recover the Hirota trilinear forms and their generalized equivalences.