Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Aliyu, Aliyu IsaScopus Q: search.filters.scopusQuartile.Q1

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Now showing 1 - 10 of 27
  • Article
    Citation - WoS: 21
    Citation - Scopus: 20
    Single and Combined Optical Solitons, and Conservation Laws in (2+1)-Dimensions With Kundu-Mukherjee Equation
    (Elsevier, 2020) Li, Yongjin; Baleanu, Dumitru; Aliyu, Aliyu Isa
    In this work, the celebrated (2 + 1)-dimensional Kundu-Mukherjee-Naskar equation (KMNE) proposed to govern the soliton dynamics in (2 + 1)-dimensions along excited resonant wave guides that is doped with Erbium atoms is studied with the aid of ansatz approach and sine-Gordon expansion method (SGEM). The integration algorithms revealed both single and combined optical solitons of the model. These solitons are reported as bright, dark, combined dark-bright and singular solitons. The combined dark-bright and combined singular soliton solutions of the KMNE are to the best of our knowledge reported for the first time in this paper. These solutions supplements the existing ones in the literature. Additionally, we studied the conservation laws (Cls) of the equation by applying the multipliers approach and report the non-trivial fluxes associated with the equation. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons.
  • Article
    Citation - WoS: 38
    Citation - Scopus: 39
    Combined Optical Solitary Waves and Conservation Laws For. Nonlinear Chen-Lee Equation in Optical Fibers
    (Elsevier Gmbh, Urban & Fischer verlag, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    This paper obtains a combined optical solitary wave solution that is modeled by nonlinear Chen-Lee-Liu equation (NCLE) which arises in the context of temporal pulses along optical fibers associated with the self-steepening nonlinearity using the complex envelope function ansatz. The novel combined solitary wave describes bright and dark solitary wave properties in the same expression. The intensity and the nonlinear phase shift of the combined solitary wave solution are reported. Moreover, the Lie point symmetry generators or vector fields of a system of partial differential equations (PDEs) which is acquired by transforming the NCLE to a real and imaginary parts are derived. It is observed that the obtained 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 conservation laws (Cis) for the system using the general Cls theorem. Numerical simulation and physical interpretations of the obtained results are demonstrated with interesting figures showing the meaning of the acquired results. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the NCLE. (C) 2017 Elsevier GmbH. All rights reserved.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 23
    Optical Solitons for Triki-Biswas Equation by Two Analytic Approaches
    (Amer inst Mathematical Sciences-aims, 2020) Alshomrani, Ali S.; Inc, Mustafa; Baleanu, Dumitru; Aliyu, Aliyu Isa
    The present study is devoted to using two analytic approaches to study the Triki-Biswas equation (TBE). The TBE model plays a vital role in propagation of short pulses of width around regions of sub-10 fs in optical. The analytic approaches used are the sine-Gordon expansion (SGEM) and the Riccatti Bernoulli sub-ODE (RBSO) methods. Chirped kink-type, bright envelope and singular solitons are formally derived.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 16
    Optical and Singular Solitary Waves To the Pnlse With Third Order Dispersion in Kerr Media Via Two Integration Approaches
    (Elsevier Gmbh, Urban & Fischer verlag, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    In this paper, the sine-Gordon expansion method (SGEM) and the generalized tanh (GTM) methods are employed to find the optical solitary wave solutions to the perturbed nonlinear Schrodinger equation (PNLSE) with Kerr law nonlinearity describing the propagation of optical solitary waves in nonlinear optical fibers. The dark, bright, dark-bright and dark-singular optical solitary waves are retrieved. Additionally, singular solitary waves are also derived as by-products of the integration scheme. Physical interpretations of the obtained results are demonstrated with interesting figures. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNLSE. (C) 2018 Elsevier GmbH. All rights reserved.
  • 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: 51
    Citation - Scopus: 56
    Optical Solitons for Complex Ginzburg-Landau Model in Nonlinear Optics
    (Elsevier Gmbh, Urban & Fischer verlag, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    This paper studies the complex Ginzburg-Landau equation (CGLE) which models soliton propagation in the presence of detuning factor in nonlinear optics. Dark, bright, dark-singular and a new dark-bright optical soliton solutions to the model are derived using the sine-Gordon equation method (SGEM). Singular soliton solutions are also celebrated. The model is studied with Kerr law, quadratic-cubic law and parabolic laws nonlinear fibers. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CGLE. (C) 2017 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: 104
    Citation - Scopus: 107
    Time-Fractional Cahn-Allen and Time-Fractional Klein-Gordon Equations: Lie Symmetry Analysis, Explicit Solutions and Convergence Analysis
    (Elsevier Science Bv, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa; Isa Aliyu, Aliyu
    This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn-Allen (CA) and time-fractional Klein-Gordon (KG) equations with Riemann-Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented. (C) 2017 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 63
    Citation - Scopus: 71
    Lie Symmetry Analysis, Explicit Solutions and Conservation Laws for the Space-Time Fractional Nonlinear Evolution Equations
    (Elsevier, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
    This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations. Some interesting figures for the obtained explicit solutions are presented. (C) 2018 Elsevier B.V. All rights reserved.