Exact solutions for power-law regularized long-wave and R(m, n) equations with time-dependent coefficients

The aim of this paper is to present solitary wave solution of two different forms of regularized long-wave equation with time-dependent coefficients that models shallow-water waves in fluid dynamics and some phenomena in elastic media, optic fibres and plasma physics. The simplest equation method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving nonlinear evolution equations with time-dependent coefficients in mathematical physics.