The decomposition method for solving (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation

Abstract

We study the solitary-wave solutions of the (2 + 1)-dimensional Boussinesq equation u tt − u xx − u yy −( u 2) xx − u xxxx =0 and (3 + 1)-dimensional KP equation u xt −6 u x 2+6 uu xx − u xxxx − u yy − u zz =0. In this paper by considering the decomposition scheme, we first obtain the exact solitary-wave solutions of the (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation for the initial conditions without using any classical transformations and then its numerical solutions are constructed without using any discretization technique. The numerical solutions are compared with the known analytical solutions. Its remarkable accuracy is finally demonstrated in the study of (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation.