Matematik Bölümü

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Citation - WoS: 5
Citation - Scopus: 6
Analytical, Numerical and Experimental Observation of Isolated Branches of Periodic Orbits in 1dof Mechanical Parametric Oscillator
(Academic Press Ltd- Elsevier Science Ltd, 2024) Kudra, Grzegorz; Witkowski, Krzysztof; Wasilewski, Grzegorz; Jarad, Fahd; Awrejcewicz, Jan; Junaid-U-Rehman, Muhammad
The aim of this study is to investigate the dynamic properties of an existing experimental stand of 1DOF mechanical parametric oscillator, with a focus on approximate analytical solutions of the observed isolated branches of periodic orbits. The experimental stand involves a cart moving along a rolling guide, with the stiffness consisting of two components: a time-varying linear element created by a rotating rod with a rectangular cross-section and a nonlinear hardening stiffness caused by magnetic springs. It was demonstrated that a rolling bearing's nonlinear resistance to motion consists of viscous damping and a second component analytically compared to dry friction. The study utilises multiple scales and harmonic balancing methods to provide analytical solutions. It is then successfully validated using numerical simulations and experimental data. The study investigates how dry friction influences oscillator response and applies the modified Mathieu-Duffing equation to represent the system's dynamics. Different branches of periodic orbits are researched to determine their function in energy harvesting and mechanical system improvement. This research demonstrates the distinctions across analytical, numerical, and experimental methodologies, providing a comprehensive understanding of investigating intricate nonlinear systems.
Citation - WoS: 40
Citation - Scopus: 48
Dispersive Optical Solitons and Modulation Instability Analysis of Schrodinger-Hirota Equation With Spatio-Temporal Dispersion and Kerr Law Nonlinearity
(Academic Press Ltd- Elsevier Science Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the perturbed nonlinear Schrodinger-Hirota equation (SHE) with spatio-temporal dispersion (STD) and Kerr law nonlinearity in optical fibers. The integration algorithm is the Sine-Gordon equation method (SGEM). Furthermore, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis and the MI gain spectrum is got. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 34
Citation - Scopus: 34
Novel Optical Solitary Waves and Modulation Instability Analysis for the Coupled Nonlinear Schrodinger Equation in Monomode Step-Index Optical Fibers
(Academic Press Ltd- Elsevier Science Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
This paper addresses the coupled nonlinear Schrodinger equation (CNLSE) in monomode step-index in optical fibers which describes the nonlinear modulations of two monochromatic waves, whose group velocities are almost equal. A class of dark, bright, dark bright and dark-singular optical solitary wave solutions of the model are constructed using the complex envelope function ansatz. Singular solitary waves are also retrieved as bye products of the in integration scheme. This naturally lead to some constraint conditions placed on the solitary wave parameters which must hold for the solitary waves to exist. The modulation instability (MI) analysis of the model is studied based on the standard linear-stability analysis. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CNLSE. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 44
Citation - Scopus: 43
Optical Soliton Solutions for the Higher-Order Dispersive Cubic-Quintic Nonlinear Schrodinger Equation
(Academic Press Ltd- Elsevier Science Ltd, 2017) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
In this paper, we analyze new optical soliton solutions to the higher-order dispersive cubic-quintic nonlinear Schrodinger equation (NLSE) using three integration schemes. The schemes used in this paper are modified tanh-coth (MTC), extended Jacobi elliptic function expansion (EJEF), and two variable (G '/G,1/G)-expansion methods. We obtain new solutions that to the best of our knowledge do not exist previously. The obtained solutions includes bright, dark, combined bright-dark, singular as well as periodic waves solitons. The obtained solutions may be used to explain and understand the physical nature of the wave spreads in the most dispersive optical medium. Some interesting figures for the physical interpretation of the obtained solutions are also presented. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 69
Citation - Scopus: 69
Optical Solitons and Modulation Instability Analysis of an Integrable Model of (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation
(Academic Press Ltd- Elsevier Science Ltd, 2017) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
This paper addresses the nonlinear Schrbdinger type equation (NLSE) in (2+1)-dimensions which describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) with anisotropic and bilinear interactions in the semiclassical limit. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the generalized tanh methods. Dark, dark-bright or combined optical and singular soliton solutions of the equation are derived. Furthermore, the modulational instability (MI) is studied based on the standard linear-stability analysis and the MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 25
Citation - Scopus: 26
Optical Solitons and Modulation Instability Analysis With (3+1)-Dimensional Nonlinear Shrodinger Equation
(Academic Press Ltd- Elsevier Science Ltd, 2017) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
This paper addresses the (3 + 1)-dimensional nonlinear Shrodinger equation (NLSE) that serves as the model to study the propagation of optical solitons through nonlinear optical fibers. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the solitary wave ansatz with Jaccobi elliptic function methods, we present the exact dark, bright and dark-bright or combined optical solitons to the model. The intensity as well as the nonlinear phase shift of the solitons are reported. The modulation instability aspects are discussed using the concept of linear stability analysis. The MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 32
Citation - Scopus: 33
Optical Solitons and Stability Analysis of the Nlse With Anti Cubic Nonlinearity
(Academic Press Ltd- Elsevier Science Ltd, 2017) Inc, Mustafa; Baleanu, Dumitru; Asian, Ebru Cavlak
In this work, the Jacobi elliptic functions are used to obtain the optical solitons for NLSE with anti -cubic nonlinearity. As a result of the operations, dark and bright optical solitons are obtained. The stability analysis for the governing equation is analyzed and investigated. The constraint conditions for the existence of soliton are also determined. Three dimensional figures and the corresponding contour plots for the obtained solutions are plotted. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 46
Citation - Scopus: 49
Optical Solitons To the Resonance Nonlinear Schrodinger Equation by Sine-Gordon Equation Method
(Academic Press Ltd- Elsevier Science Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
In this paper, we examined the optical solitons to the resonant nonlinear Schrodinger equation (R-NLSE) which describes the propagation of solitons through optical fibers. Three types of nonlinear media fibers are studied. They are; quadratic-cubic law, Kerr law and parabolic law. Dark, bright, dark-bright or combined optical and singular soliton solutions are derived using the sine-Gordon equation method (SGEM). The constraint conditions that naturally fall out of the solution structure which guarantee the existence of these solitons are also reported. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 27
Citation - Scopus: 30
Optical Solitons, Nonlinear Self-Adjointness and Conservation Laws for the Cubic Nonlinear Shrodinger's Equation With Repulsive Delta Potential
(Academic Press Ltd- Elsevier Science Ltd, 2017) Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru
In this paper, the complex envelope function ansatz method is used to acquire the optical solitons to the cubic nonlinear Shrodinger's equation with repulsive delta potential (delta-NLSE). The method reveals dark and bright optical solitons. The necessary constraint conditions which guarantee the existence of the solitons are also presented. We studied the delta-NLSE by analyzing a system of partial differential equations (PDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system and prove that the system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conserved vectors for the system using the general Cls theorem presented by Ibragimov. Some interesting figures for the acquired solutions are also presented. (C) 2017 Elsevier Ltd. All rights reserved.

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