The Application of the Homotopy Perturbation Method and the Homotopy Analysis Method to the Generalized Zakharov Equations

Table 1

The HPM results for 𝐸(𝑥,𝑡) for the first three approximation in comparison with the analytical solution with initial conditions (3.11) when 𝑘=0.05,𝑘₁=1,𝑠=0.33,𝛽=1.

𝑡𝑖
𝑥𝑖	0.1	0.2	0.3	0.4	0.5
0.1	4.4605×10^−14	3.99649×10^−12	4.88487×10^−11	2.82493×10^−10	1.0943×10^−9
0.2	1.20054×10^−17	3.04251×10^−12	4.29073×10^−11	2.60288×10^−10	1.03179×10^−9
0.3	6.81758×10^−14	1.71124×10^−12	3.5057×10^−11	2.32051×10^−10	9.54569×10^−10
0.4	1.59939×10^−13	3.07249×10^−15	2.53001×10^−11	1.97794×10^−10	8.62668×10^−10
0.5	2.7525×10^−13	2.08147×10^−12	1.36395×10^−11	1.57525×10^−10	7.56107×10^−10