Analysis of rational solutions to the (3+1) dimensional nonlinear evolution equations

This article discusses the types of rational solutions obtained by the test function of the (3+1) dimensional nonlinear evolution equation, which consists of N positive quadratic functions. We can get that there are three different types of waves: the lump-type waves, the linear rogue waves, and the solitary waves in different planes, using the long-wave limit method. In order to facilitate the discussion of different cases of solutions and solve the problem that the solutions for the superposition of more than three positive quadratic functions cannot be calculated by computer, quadratic matrices are introduced, consisting of vectors formed by the coefficients of the variables. Finally, we give examples of three different solutions to the (3+1) dimensional B-type Kadomtsev-Petviashvili equation, calculate the corresponding physical quantities, and draw the corresponding physical images.