Dynamics of Different Nonlinearities to the Perturbed Nonlinear Schrödinger Equation via Solitary Wave Solutions with Numerical Simulation

This paper investigates the solitary wave solutions for the perturbed nonlinear Schrödinger equation with six different nonlinearities with the essence of the generalized classical derivative, which is known as the beta derivative. The aforementioned nonlinearities are known as the Kerr law, power,...

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Bibliographic Details
Published in:Fractal and fractional Vol. 5; no. 4; p. 213
Main Authors: Zafar, Asim, Raheel, Muhammad, Zafar, Muhammad Qasim, Nisar, Kottakkaran Sooppy, Osman, Mohamed S., Mohamed, Roshan Noor, Elfasakhany, Ashraf
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.12.2021
Subjects:
beta derivative operator
Nonlinearity
Partial differential equations
perturbed nonlinear Schrödinger equation
Power law
Schrodinger equation
solitary wave solutions
Solitary waves
Velocity
ISSN:2504-3110, 2504-3110
Online Access:Get full text
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Summary:This paper investigates the solitary wave solutions for the perturbed nonlinear Schrödinger equation with six different nonlinearities with the essence of the generalized classical derivative, which is known as the beta derivative. The aforementioned nonlinearities are known as the Kerr law, power, dual power law, triple power law, quadratic–cubic law and anti-cubic law. The dark, bright, singular and combinations of these solutions are retrieved using an efficient, simple integration scheme. These solutions suggest that this method is more simple, straightforward and reliable compared to existing methods in the literature. The novelty of this paper is that the perturbed nonlinear Schrödinger equation is investigated in different nonlinear media using a novel derivative operator. Furthermore, the numerical simulation for certain solutions is also presented.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract5040213