Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Yusuf, AbdullahiPublisher: search.filters.publisher.Elsevier Gmbh

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Now showing 1 - 7 of 7
  • Article
    Citation - WoS: 40
    Citation - Scopus: 41
    Dark and Singular Optical Solitons for the Conformable Space-Time Nonlinear Schrodinger Equation With Kerr and Power Law Nonlinearity
    (Elsevier Gmbh, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
    This paper extracts novel dark and singular optical solitons for the conformable space time nonlinear Schrodinger equation (CSTNLSE) with Kerr and power law nonlinearity by two integration schemes. The integration schemes are generalized tanh (GT), and Bernoulli (BL) sub-ODE methods. The constraints conditions for the existence of solitons are reported. The newly introduced fractional derivative called conformable derivative is used for extracting the soliton solutions. Numerical simulations of some of the obtained solutions are also presented. (C) 2018 Elsevier GmbH. All rights reserved.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 15
    Gray Optical Soliton, Linear Stability Analysis and Conservation Laws Via Multipliers To the Cubic Nonlinear Schrodinger Equation
    (Elsevier Gmbh, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    This paper addresses the cubic nonlinear Schrodinger equation with a bounded potential (CNLSE) which describes optical solitary waves propagation properties in optical fiber. A gray optical soliton solution of this equation is retrieved for the first time by adopting an appropriate solitary wave ansatz which play a vital role in understanding various physical phenomena in nonlinear systems. The integration lead to a constraint condition on the solitary wave parameters which must hold for the soliton to exist. We studied the conservation laws (Cls) of the CNLSE by analyzing a system of partial differential equations (PDEs) obtained by transforming the equation into real and imaginary components. The multiplier approach is employed to retrieve the conservation laws. Moreover, the modulation instability (MI) analysis of the model is studied by employing the linear-stability analysis and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CNLSE. (C) 2018 Elsevier GmbH. All rights reserved.
  • Article
    Citation - WoS: 50
    Citation - Scopus: 51
    Optical Solitary Waves, Conservation Laws and Modulation Instability Analysis To the Nonlinear Schrodinger's Equation in Compressional Dispersive Alven Waves
    (Elsevier Gmbh, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    In this paper, the sine-Gordon equation expansion method (SGEM) is used to acquire the optical solitary waves to the nonlinear Schrodinger's equation (NLSE) that arises from compressional dispersive Alven (CDA) waves. As a result of the operations, dark, bright, dark-bright and singular optical solitary waves are derived. The solitary waves appear with all necessary constraint conditions which guarantee their existence. The Lie point symmetry generators of a system of partial differential equations (PDEs) obtained by transforming the equation into real and imaginary parts are derived. We 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 construct a set of conservation laws (Cls) for the system using the general Cls theorem presented by lbragimov. Furthermore, the modulation instability (MI) is studied based on the standard linear-stability analysis and the MI gain spectrum is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier GmbH. All rights reserved.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 17
    Dark and Combined Optical Solitons, and Modulation Instability Analysis in Dispersive Metamaterial
    (Elsevier Gmbh, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    This paper obtains the dark and dark-bright or combined optical solitons to the nonlinear schrodinger equation (NLSE) describing propagation in dispersive metamaterial in optical fibers. The integration algorithm is the complex envelope function ansatz. This naturally lead to some constraint conditions placed on the soliton parameters which must hold for the solitons to exist. The intensities and the nonlinear phase shifts of the solitons are reported. Furthermore, the modulation instability analysis (MI) is studied based on the standard linear-stability analysis and the MI gain spectrum is got. Numerical simulation of some obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier GmbH. All rights reserved.
  • Article
    Citation - WoS: 44
    Citation - Scopus: 49
    Optical Solitons for Biswas-Milovic Model in Nonlinear Optics by Sine-Gordon Equation Method
    (Elsevier Gmbh, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    This article studies the dynamics of optical solitons to the Biswas-Milovic equation (BME) which describes the dynamics of optical solitons in generalized form. There are four types of nonlinear fibers studied in this paper. They are quadratic-cubic, Kerr and Parabolic laws. The integration algorithm adopted is the Sine-Gordon equation method (SGEM). Dark, bright and dark-singular optical solitons are derived. Complex singular solitons are also reported. The obtained results have important applications in the study of solitons in optical fibers. (C) 2017 Elsevier GmbH. All rights reserved.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 21
    Optical Solitons and Stability Analysis With Spatio-Temporal Dispersion in Kerr and Quadric-Cubic Nonlinear Media
    (Elsevier Gmbh, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
    In this work, we investigate the optical solitons to the nonlinear Schrodinger equation (NISE) with spatio-temporal dispersion (STD) arising in ferromagnetic materials and optical fiber. The integration technique adopted is the Sine-Gordon expansion method (SGEM). In addition, the stability analysis of the model is performed.
  • Article
    Citation - WoS: 40
    Citation - Scopus: 35
    Dark Optical Solitons and Conservation Laws To the Resonance Nonlinear Shrodinger's Equation With Kerr Law Nonlinearity
    (Elsevier Gmbh, 2017) Yusuf, Abdullahi; Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru
    In this work, we investigate the soliton solutions to the resonant nonlinear Shrodinger's equation (R-NSE) with Kerr law nonlinearity. By adopting the Riccati-Bernoulli sub-ODE technique, we present the exact dark optical, dark-singular and periodic singular soliton solutions to the model. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. We studied the R-NSE by analyzing a system of nonlinear partial differential equations (NPDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system, then we apply the general conservation theorem to establish a set of nontrivial and nonlocal conservation laws (Cls). Some interesting figures for the acquired solutions are Cls also presented. (C) 2017 Elsevier GmbH. All rights reserved.