A VARIATIONAL PRINCIPLE OF THE NONLINEAR SCHRÖDINGER EQUATION WITH FRACTAL DERIVATIVES

Abstract

The nonlinear Schrödinger equation plays a crucial role in describing the propagation of the soliton in optical fibers. In this study, a fractal modification of the nonlinear Schrödinger equation for the discontinuous time is proposed and the fractal variational principle (VP) is developed via employing the semi-inverse method. The whole derivation process of the fractal VP is presented in detail and the correctness of the fractal VP is verified via the Euler–Lagrange equations by calculating the stationary conditions. The fractal VP established in this paper is expected to deepen our understanding of the essence of physical phenomena in fractal space.