In this work, the modified simple equation (MSE) method is applied to some class of
nonlinear PDEs, namely, a system of nonlinear PDEs, a (2 + 1)-dimensional nonlinear model gener-
ated by the Jaulent–Miodek hierarchy, and a generalized KdV equation with two power nonlinearities.
As a result, exact traveling wave solutions involving parameters have been obtained for the considered
nonlinear equations in a concise manner. When these parameters are chosen as special values,
the solitary wave solutions are derived. It is shown that the proposed technique provides a more pow-
erful mathematical tool for constructing exact solutions for a broad variety of nonlinear PDEs in
mathematical physics.