Soliton solution of the generalized modified BBM equation and the generalized Boussinesq equation

Abstract

In this paper, we obtained the topological soliton solution of the (1+1)-dimensional generalized modified Benjamin–Bona–Mahony equation and shock wave solution of the generalized Boussinesq equation. We get that solutions by using solitary wave ansatz in terms of tanh p functions. The velocity and the free parameters are the physical parameters in the soliton solutions. They can be obtained as functions of the dependent model coefficients. The domain restriction were also identified in the process. we hope that in nonlinear dynamical system these solutions will be explain some nonlinear physical phenomena.