https://doi.org/10.1140/epjp/s13360-023-04697-5
Regular Article
Dynamical properties and new optical soliton solutions of a generalized nonlinear Schrödinger equation
1
Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pukhtunkhwa, Pakistan
2
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box-65892, 11566, Riyadh, Saudi Arabia
3
School of Mathematical Sciences, Jiangsu University, 212013, Zhenjiang, Jiangsu, People’s Republic of China
4
Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, 11022801, Beirut, Lebanon
Received:
29
September
2023
Accepted:
14
November
2023
Published online:
30
November
2023
For exploring the behavior of complex two-dimensional systems, the idea of planar dynamical systems offers a potent and adaptable framework. It is simple for researchers to understand the dynamics of the system and acquire deeper insights into its behavior by visualizing trajectories in the (x,y) plane. Keeping this in mind, the complex dynamics of the nonlinear Schrödinger equation has not been explored using planar dynamical theory, in the literature. In this manuscript, the dynamical features and some new optical solitons are discussed for the considered NLSE. Using RK4 numerical technique, the dynamical features such as bifurcation, phase portraits, time series and sensitivity analysis are portrayed. Moreover, utilizing the traveling wave transformations and complete discriminant system method, some new optical solitary waves solutions are obtained which depends on trigonometric functions and Jacobi elliptic functions. These solutions are new and have not been reported in the literature for the considered equation.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
