The traveling and non-traveling wave solutions of (1+1)-dimensional Boussinesq equations with variable coefficients

Based on (G ′ /G)-expansion method, new traveling and non-traveling exact solutions of (1+1)-dimensional Boussinesq equations with variable coefficients are established. To obtain the traveling wave solution, we expand ξ(x, t) = x − V t to a more general form ξ(x, t) = f(η), η = x − V t. We also suppose the non-traveling wave solution ξ(x, t) with variable separation forms, such as ξ(x, t) = f(x) + g(t) or ξ(x, t) = f(x)g(t). Finally, a series of important novel solutions of the equations are obtained.