Rational solutions consisting of multiple lump waves and line rogue waves in different spaces of the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid

In this paper, a (3+1)-dimensional Boiti–Leon–Manana–Pempinelli equation in incompressible fluid is mainly considered to investigate the rational solutions consisting of multiple lump waves and line rogue waves in different spaces by means of the Wronskian solutions. We derive the Wronskian solution for the bilinear form. On this basis, the Mth-order lump solutions and Mth-order line rogue wave solutions are obtained from the 2Mth-order Wronskian solutions by using the elementary transformation and the method of long wave limit. It is interesting that the obtained solutions possess the structure of multiple lump waves on the (x, y) and (x, z) planes. Meanwhile, the line rogue waves are also found on the (y, z) plane. The dynamical behaviors and characteristics of the lump waves and line rogue waves are presented in virtue of numerical simulation. The method presented in this paper gives us a new perspective to derive high-order lumps and rogue waves for the high-dimensional integrable systems. All the results are helpful for us to understand the nonlinear wave phenomena existing in incompressible fluid.