Abstract: In this article, the authors simulate and study dark and bright soliton solutions of 1D and 2D regularized long wave (RLW) models. The RLW model occurred in various fields such as shallow-water waves, plasma drift waves, longitudinal dispersive waves in elastic rods, rotating flow down a tube, and the anharmonic lattice and pressure waves in liquid–gas bubble mixtures. First of all, the tanh–coth method is applied to obtain the soliton solutions of RLW equations, and thereafter, the approximation of finite domain interval is done by truncating the infinite domain interval. For computational modeling of the problems, a meshfree method based on local radial basis functions and differential quadrature technique is developed. The meshfree method converts the RLW model into a system of nonlinear ordinary differential equations (ODEs), then the obtained system of ODEs is simulated by the Runge–Kutta method. Further, the stability of the proposed method is discussed by the matrix technique. Finally, in numerical experiments, some problems are considered to check the competence and chastity of the developed method.
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