Optical soliton solutions for space fractional Schrödinger equation using similarity method

Abstract

In this paper, the similarity method is employed to solve the space-fractional Schrödinger equation, and the fractional derivative is defined in the Riesz sense. It is worth noting that the similarity method decreases the number of independent variables in the equation by one variable, so we use it to transform the fractional partial differential equation (FPDE) with two independent variables (time and space) into the fractional ordinary differential equation (FODE) in the same fractional derivative sense. The exact solution is obtained by applying a fractional Fourier transform to both sides of the transformed FODE. Based on the obtained results, different graphs of the solution are presented. The present investigation confirms the efficiency of the proposed method.

Keywords

• Similarity transformation
• Fractional Schrödinger equation
• Riesz fractional derivative
• Fractional Fourier transform