Examination of the partial differential equations by Hirota's method

In this thesis, the Hirota-bilinear method was examined. This method is applied to obtain analytical exact single-wave solutions of the nonlinear partial differential equations. 1-, 2-, 3- and multiple soliton solutions of the important equations of the mathematical physics were investigated with the help of the Hirota-bilinear method, which was used to obtain the multiple soliton solutions of such equations and introduced by R. Hirota. This method is applied to the (3+1)-dimensional generalized KP equation and (3+1)-dimensional soliton equation, respectively. Different functions are considered in order to obtain multiple soliton solutions of the equations that become a linear using this method. The solutions of the examined equations obtained by other methods were compared with the exact solutions obtained in this study. In addition, two and three dimensional graphs are drawn to understand the physical behavior of the obtained multiple (soliton) exact solutions of the (3+1) dimensional generalized KP equation and the (3+1) dimensional soliton equation.