To read this content please select one of the options below:

Novel solitary wave solution of the nonlinear fractal Schrödinger equation and its fractal variational principle

Yasir Khan (Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin, Saudi Arabia)

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Article publication date: 1 March 2021

Issue publication date: 6 April 2021




The nonlinear Schrödinger equation plays a vital role in wave mechanics and nonlinear optics. The purpose of this paper is the fractal paradigm of the nonlinear Schrödinger equation for the calculation of novel solitary solutions through the variational principle.


Appropriate traveling wave transform is used to convert a partial differential equation into a dimensionless nonlinear ordinary differential equation that is handled by a semi-inverse variational technique.


This paper sets out the Schrödinger equation fractal model and its variational principle. The results of the solitary solutions have shown that the proposed approach is very accurate and effective and is almost suitable for use in such problems.

Practical implications

Nonlinear Schrödinger equation is an important application of a variety of various situations in nonlinear science and physics, such as photonics, the theory of superfluidity, quantum gravity, quantum mechanics, plasma physics, neutron diffraction, nonlinear optics, fiber-optic communication, capillary fluids, Bose–Einstein condensation, magma transport and open quantum systems.


The variational principle of the Schrödinger equation without the Lagrange multiplier method in the sense of the fractal calculus is developed for the first time in the literature to the best of the author's understanding.



The author is grateful to the referees, whose comments and suggestions improved the presentation and value of the article. The author extends their appreciation to the Deanship of Scientific Research, University of Hafr AlBatin for funding this work through the research group project no. (G-108-2020).


Khan, Y. (2021), "Novel solitary wave solution of the nonlinear fractal Schrödinger equation and its fractal variational principle", Multidiscipline Modeling in Materials and Structures, Vol. 17 No. 3, pp. 630-635.



Emerald Publishing Limited

Copyright © 2021, Emerald Publishing Limited

Related articles