In this work, we establish the exact solutions to the modified forms of Degasperis–Procesi (DP) and Camassa–Holm (CH) equations. The generalized (G’/G)-expansion and generalized tanh-coth methods were used to construct solitary wave solutions of nonlinear evolution equations. The generalized (G’/G)-expansion method presents a wider applicability for handling nonlinear wave equations. It is shown that the (G’/G)-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.