Numerical Soliton Solutions of Fractional Modified (2 + 1)-Dimensional Konopelchenko–Dubrovsky Equations in Plasma Physics

Abstract

In this paper, the time-fractional modified (2 + 1)-dimensional Konopelchenko–Dubrovsky equations have been solved numerically using the Kansa method, in which the multiquadrics is used as radial basis function. To achieve this, a numerical scheme based on finite difference and Kansa method has been proposed. The stability and convergence of the proposed time-discretized scheme are theoretically proven. Also, the solitary wave solutions have been obtained by using Kudryashov technique. The computed results are compared with the exact solutions as well as with the soliton solutions obtained by Kudryashov technique to show the accuracy of the proposed method.