Numerical soliton solutions of fractional (2 + 1)-dimensional Nizhnik–Novikov–Veselov equations in nonlinear optics

Abstract

In this paper, time-fractional (2 + 1)-dimensional Nizhnik–Novikov–Veselov equations have been solved numerically utilizing the Kansa method, in which the multiquadrics are taken as radial basis function. To attain this, a numerical scheme based on finite difference and Kansa method has been proposed. In addition, the soliton solutions have been obtained by employing Kudryashov method and tanh method for comparison purpose with the obtained numerical solutions. The numerical examples are given to demonstrate the accuracy and applicability of the proposed method.