A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation

摘要

We consider solitary-wave solutions of the generalized regularized long-wave (RLW) equation ut+ux+α(up)x−βuxxt=0. In this paper by considering the decomposition scheme, we first obtain the exact solitary-wave solutions of the generalized RLW equation for the initial condition 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 some values p⩾2 of the generalized RLW equation.