Bifurcations, chaotic behavior, sensitivity analysis, and various soliton solutions for the extended nonlinear Schrödinger equation

In this manuscript, our primary objective is to delve into the intricacies of an extended nonlinear Schrödinger equation. To achieve this, we commence by deriving a dynamical system tightly linked to the equation through the Galilean transformation. We then employ principles from planar dynamical sy...

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Bibliographic Details
Published in:Boundary value problems Vol. 2024; no. 1; p. 15
Main Authors: ur Rahman, Mati, Sun, Mei, Boulaaras, Salah, Baleanu, Dumitru
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 19.01.2024
Hindawi Limited
SpringerOpen
Subjects:
Analysis
Approximations and Expansions
Bifurcation theory
Difference and Functional Equations
Dynamic systems theory
Dynamical systems
Galilean transformation
Initial conditions
Mathematics
Mathematics and Statistics
Nonlinear equations
Ordinary Differential Equations
Partial Differential Equations
Polynomials
Runge-Kutta method
Schrodinger equation
Schrödinger equation
Sensitivity analysis
Solitary waves
System theory
Traveling wave solutions
Traveling waves
Nonlinear equations
Galilean transformation
Traveling wave solutions
Schrödinger equation
ISSN:1687-2770, 1687-2762, 1687-2770
Online Access:Get full text
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Summary:In this manuscript, our primary objective is to delve into the intricacies of an extended nonlinear Schrödinger equation. To achieve this, we commence by deriving a dynamical system tightly linked to the equation through the Galilean transformation. We then employ principles from planar dynamical systems theory to explore the bifurcation phenomena exhibited within this derived system. To investigate the potential presence of chaotic behaviors, we introduce a perturbed term into the dynamical system and systematically analyze the extended nonlinear Schrödinger equation. This investigation is further enriched by the presentation of comprehensive two- and 3D phase portraits. Moreover, we conduct a meticulous sensitivity analysis of the dynamical system using the Runge–Kutta method. Through this analytical process, we confirm that minor fluctuations in initial conditions have only minimal effects on solution stability. Additionally, we utilize the complete discrimination system of the polynomial method to systematically construct single traveling wave solutions for the governing model.
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ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-024-01825-7