On the Soliton Solution and Jacobi Doubly Periodic Solution of the Fractional Coupled Schrodinger-KdV Equation by a Novel Approach

摘要

In this paper, fractional coupled Schrodinger-Korteweg-de Vries equation (or Sch-KdV) equation with appropriate initial values has been solved by using a new novel method. The fractional derivatives are described in the Caputo sense. By using the present method, we can solve many linear and nonlinear coupled fractional differential equations. Basically, the present method originated from generalized Taylor's formula [1]. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of fractional coupled Schrodinger-KdV equation. Numerical solutions are presented graphically to show the reliability and efficiency of the method. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. The convergence of the method as applied to Sch-KdV is illustrated numerically as well as derived analytically. Moreover, the results are compared with those obtained by the Adomian decomposition method (ADM).