Modified Hirota bilinear method to (3+1)-D variable coefficients generalized shallow water wave equation

Variable coefficients (3+1)-generalized shallow water wave equation (GSWE) is investigated via modified Hirota bilinear method. This method is presented for the first time. Compared with other methods, it solves solution without setting solution and calculates transformations without making logarithmic transformations. The rational transformation is first utilized to transform GSWE. According to homogeneous balance principle, the relation between F and G in rational transformation can be calculated by utilizing. Solutions that included rogue wave solutions, interaction solutions, breather solutions and so on, are obtained and depicted graphically. Figures are given out to the dynamic characteristics of the solution. Furthermore, the results obtained demonstrate that this approach is more direct, generalized, effective and holds for many nonlinear partial differential equations.