We have solved the fKdV equation and the 5th-order fKdV equation numerically.
The solutions of the 5th-order fKdV equation at t = 400 for Bo = 0.3, using N = 1536 and N = 3072, are presented in Fig.
We can easily verify that the fKdV equation (9) is invariant by the simultaneous change of the variables' sign ([eta] [right arrow] -[eta]', x [right arrow] -x') and the parameter (Bo [right arrow] 2/3 - Bo').
We first compare the solution of the Euler equations with that of the fKdV equation (Fig.
We next compare the solution of the Euler equations with that of the 5th-order fKdV equation (Fig.
Comparison of results with the weakly nonlinear theories reveals that the fKdV equation is applicable to the cases with strong capillary effects (Bo [much greater than] 1/3), while the 5th-order fKdV equation with a 5th-order dispersion term is qualitatively applicable to the case of Bo [equivalent] 1/3, for which the fKdV equation is not applicable.
The HAM of the fKdV equation (3) is presented in Section 2.
Further to this research output, we will now apply HAM to solve different fKdV equations based on various forcing terms.
Using Different Forcing Terms for fKdV. For simplicity, we let [alpha] = -6 and [beta] = 1 for all the cases studied below.
As a whole it can be concluded that the wave changes tremendously over time with the sine force incorporated in fKdV equation.
Comparison of fKdV HAM Solution with Zhao and Guos Analytical Solution.