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

Figure 1

Comparison between the exact solution, the HPM solution, the ADM solution, and the HAM solution for 𝐸(𝑥,𝑡) with initial conditions (3.11) when 𝑘=0.05,𝑘₁=1,𝑠=0.33,𝛽=1,ℏ=−1.

(a) The exact solution for |𝐸|²

(b) The HPM solution for |∑³_𝑘=0𝐸²_𝑘|

(c) The ADM solution for |∑⁶_𝑘=0𝐸²_𝑖|

(d) The HAM solution for |𝐸|² for the 8th order