Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme

Abstract

This paper deals with the study of fractional Kundu-Eckhaus equation (FKEE) and fractional massive Thirring problem (FMTP) that appear in the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. Since the variational iteration method involves integration, the Laplace transform involves convolution theorem in recurrence relation to derive the series solution. To avoid some assumptions and hypothesis, we apply a two-scale approach for such a nonlinear complex model. The fractional differential equation may be transformed into its partner equation using He’s fractional complex transform, and then, the nonlinear elements can be readily handled using the homotopy perturbation method (HPM). Numerical results are derived in a rapid converge series form to improve the accuracy of the scheme greatly. Graphical representations and error distribution show that the two-scale approach is a very convenient tool.