In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in the mathematical physics via the (1+1)-dimensional Boussinesq equation by using the following two methods: (i) A further improved ($frac{G}{G}$) - expansion method, where $G=G({xi})$ satisfies the auxiliary ordinary differential equation $[G^{prime}({xi})]^2=aG^2({xi})+bG^4({xi})+cG^6({xi})$, where ${xi}=x-Vt$ while $a$, $b$, $c$ and $V$ are constants. (ii) The well known extended tanh-function method. We show that some of the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before which gives more exact solutions than the second method (ii).