APPLICATION OF He’s VARIATIONAL ITERATION METHOD AND ADOMIAN’S DECOMPOSITION METHOD TO PROCHHAMMER CHREE EQUATION

The model for α = 1, β = 1/(m + 1) and γ = 0 was studied by Bagolubasky and Clarkson et al. A second model for α = 0, β = −(1/2) and γ = 0 was studied by Parker and solitary wave solutions were obtained as well. However, a third model was investigated in Refs. 10 and 11 for m = 1 and m = 2 where explicit solitary wave solutions and kinks solutions were derived. For m ≥ 1, we get consecutive exponents and odd exponents for u and u, respectively. The tanh–coth and the sine–cosine methods were represented by Wazwaz for kinks, solitons and periodic solutions of the Prochhammer–Chree equations. Most of the physical and engineering phenomena are modeled in the form of nonlinear equations. Finding the reliable procedure to handle nonlinearity is a significant problem which most of scientists deal with.