Research Article

Dynamical system of optical soliton parameters by variational principle (super-Gaussian and super-sech pulses)

¹ Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
² Basic Science Department, Faculty of Computers and Artificial Intelligence, Modern University for Technology & Information, Cairo 11585, Egypt
³ Basic Science Department, Higher Institute of Foreign Trade & Management Sciences, New Cairo Academy, Cairo 379, Egypt
⁴ Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA
⁵ Mathematical Modeling and Applied Computation (MMAC) Research Group, Center of Modern Mathematical Sciences and their Applications (CMMSA), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
⁶ Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati 800201, Romania
⁷ Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, South Africa
⁸ Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey
⁹ Department of Mathematics, Near East University, 99138 Nicosia, Cyprus
¹⁰ Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008, Romania
¹¹ Department of Business Administration, Faculty of Economics and Business Administration, Dunarea de Jos University of Galati, 59–61 Nicolae Balcescu Street, 800001 Galati, Romania

^* Corresponding author: luminita.moraru@ugal.ro

Received: 3 June 2023
Accepted: 6 July 2023

Abstract

The parameter dynamics of super-sech and super-Gaussian pulses for the perturbed nonlinear Schrödinger’s equation with power-law nonlinearity is obtained in this article. The variational principle successfully recovers this dynamical system. The details of the variational principle with the implementation of the Euler–Lagrange’s equation to the nonlinear Schrödinger’s equation with power-law of nonlinearity described in this paper have not been previously reported.