New exact solutions to the generalized shallow water wave equation

Abstract

In this work, we study the generalized shallow water wave equation to obtain novel solitary wave solutions. The application of this non-linear model can be found in tidal waves, weather simulations, tsunami prediction, river and irrigation flows, etc. To obtain the new exact solutions of the considered model, we have applied a novel analytical technique namely $\left(\frac{G'}{G'+G+A}\right)$--expansion method. Using the aforementioned method and computational software, we have obtained different kinds of periodic and singular solitary wave solutions of the generalized shallow water wave equation. The obtained solutions are exponential function and trigonometric function solutions. Using 2-D and 3-D plots of the wave solutions, the dynamic behaviors of the developed solutions are displayed. The retrieved solutions validated the effectiveness and robustness of the proposed technique.

Figures (4)

• Figure 1: 3D and 2D graphical representation of solution corresponding to Eq. (\ref{['eq:16']}) for $B = 1, C = 0.1, k_1=k_2 = 1$.
• Figure 2: 3D and 2D graphical representation of solution corresponding to Eq. (\ref{['eq:17']}) for $B = 1, C = 1.1, k_1=k_2 = 1$.
• Figure 3: 3D and 2D graphical representation of solution corresponding to Eq. (\ref{['eq:18']}) for $B =1, C = 0.1, k_1 =k_2 = 1$.
• Figure 4: 3D and 2D graphical representation of solution corresponding to Eq. (\ref{['eq:19']}) for $B =1, C = 1.1, k_1 =1.5, k_2 = 1$.