A VARIATIONAL PRINCIPLE OF THE NONLINEAR SCHRÖDINGER EQUATION WITH FRACTAL DERIVATIVES

Wen-Lei Li, Song-Hao Chen and Kang-Jia Wang
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Wen-Lei Li: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Song-Hao Chen: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Kang-Jia Wang: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 07, 1-6

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.

Keywords: Semi-Inverse Method; Fractal Nonlinear Schrödinger Equation; Variational Principle; Lagrange Function; Stationary Condition (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500690

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