Comment on ‘two new integrable fourth-order nonlinear equations: multiple soliton solutions and multiple complex soliton solutions’

Classification of single-wave and bi-wave motion through fourth-order equations generated from the Ito model

“…This equation describes the behavior of a one-dimensional fluid system that is subject to random fluctuations and has found applications in various fields such as turbulence, wave propagation, and reaction-diffusion processes. Tian and Zhang [2] introduced a new potential function θ = θ(x, t) that satisfies the relation u(x, t) = θ x (x, t) which converts the Ito equation (1.1) into the following form q q q q q + + -= f t…”

“…By examining the findings of [2], it can be noted that Wazwaz's equations are particular instances of (1.4). Specifically, when g(t) takes a value of zero, the resulting equation is the first fourth-order integrable equation (1.5).…”

“…Similarly, when g(t) is assigned a value of β, the equation reduces to the second fourth-order integrable equation (1.6). Therefore, Tian and Zhang [2] have established that both (1.5) and (1.6) are potential formulations of the Ito equation (1.4).…”