New variational theory for coupled nonlinear fractal Schrödinger system

Abstract

PurposeThe purpose of this paper is the coupled nonlinear fractal Schrödinger system is defined by using fractal derivative, and its variational principle is constructed by the fractal semi-inverse method. The approximate analytical solution of the coupled nonlinear fractal Schrödinger system is obtained by the fractal variational iteration transform method based on the proposed variational theory and fractal two-scales transform method. Finally, an example illustrates the proposed method is efficient to deal with complex nonlinear fractal systems.Design/methodology/approachThe coupled nonlinear fractal Schrödinger system is described by using the fractal derivative, and its fractal variational principle is obtained by the fractal semi-inverse method. A novel approach is proposed to solve the fractal model based on the variational theory.FindingsThe fractal variational iteration transform method is an excellent method to solve the fractal differential equation system.Originality/valueThe author first presents the fractal variational iteration transform method to find the approximate analytical solution for fractal differential equation system. The example illustrates the accuracy and efficiency of the proposed approach.