Higher-order hybrid waves for the (2 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid via the modified Pfaffian technique

Fluids, as a phase of matter including liquids, gases and plasmas, are seen to be common in nature, the study of which helps the design in the related industries. In this paper, we optimize the Pfaffian technique and investigated the Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid. Higher-order hybrid solutions consisting of the L lumps, M breathers and N solitons are constructed with L, M and N being positive integers. Relative extrema of the breather and lump are presented, respectively. Breather is found to be localized along the curve $$a_1 x+b_1 \varphi (y)+\omega _1 t+\xi _1=0$$ and periodic along the curve $$\alpha _1 x+\beta _1 \varphi (y)+\gamma _1 t+\theta _1=0$$ . Under the lump existence condition, higher-order rogue wave solutions do not exist. Hybrid solutions composed of breathers, lumps and solitons are illustrated graphically. It can be found that when certain parameters are chosen, the breather, lump and soliton included in the hybrid solutions possess the same properties as those of the breather and lump solutions.