A practical and powerful approach to potential KdV and Benjamin equations

Implementation of variational iteration method for various types of linear and nonlinear partial differential equations

“…5 to test the correctness and dependability of the VIM solution for the p-KdV equation. The 4-order approximation solution derived by VIM compared to the exact solution and the reduced differential transform method (RDTM) solution [37] is summarized in Table 1 and Figures 1 and 2 for different values of x, t ∈ [0,1]. The results we obtained are very close to the exact solution as well as the RDTM solution.…”

“…We look at how successfully potential Korteweg-De-Vries equation (p-KDV) approximation solutions are implemented and checked using the method that we suggested in section 2. In order to accomplish this, we make use of the nonlinear p-KDV as a physical problem [37] in (4). where 𝑢 (𝑥, 𝑡) represents the dependent variable, 𝑥 and 𝑡 represent the independent variables, and the parameters 𝑎 and 𝑏 are nonzero real constants.…”

“…The calculator in VIM is essential and accessible [36]. The VIM eliminates the difficulties of measuring Adomian polynomials in ADM [37], giving it a considerable advantage over ADM. The VIM also eliminates the need for discretization in numerical methods, resulting in an approximate solution with high accuracy, minimal calculation, and no physically unreasonable assumptions.…”

Soliton Solutions of Generalized Third Order Time‐Fractional KdV Models Using Extended He‐Laplace Algorithm

“…e proposed approach is applied to three KdV models, namely, Korteweg-de Vries-Burgers (KdVB) [31], potential Korteweg-de Vries (p-KdV) [32], and time-fraction dispersive KdV equation [31]. e generalized KdVB equation was proposed by Su and Gardner in 1969 [33] by combining the classical KdV equation [18] with the Burgers equation [34].…”

“…KdVB equation depicts several physical phenomena like the flow of liquids containing gas bubbles, propagation of waves in an elastic tube filled with a viscous fluid, plasma waves, and propagation of bores in shallow water etc. On the other hand, the p-KdV equation [32] replicates waves on much greater frequency such as tsunami waves.…”