Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Inc, MustafaSubject: search.filters.subject.Cls

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Now showing 1 - 9 of 9
  • Article
    Citation - WoS: 21
    Citation - Scopus: 23
    Optical Solitons, Conservation Laws and Modulation Instability Analysis for the Modified Nonlinear Schrodinger's Equation for Davydov Solitons
    (Taylor & Francis Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    In this paper, the optical solitons to the modified nonlinear Schrodinger's equation for davydov solitons are investigate. The modified F-expansion method is the integration technique employed to achieve this task. This yielded a combined and other soliton solutions. The Lie point symmetry generators of a system of partial differential equations acquired by decomposing the equation into real and imaginary components 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 local conservation laws (Cls) for the system using the general Cls theorem presented by Ibragimov. Furthermore, the modulation instability (MI) is analyzed 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.
  • 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.
  • Article
    Citation - WoS: 111
    Citation - Scopus: 113
    Lie Symmetry Analysis, Exact Solutions and Conservation Laws for the Time Fractional Caudrey-Dodd Equation
    (Elsevier, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru
    In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK. (C) 2017 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 32
    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.
  • Article
    Citation - WoS: 52
    Citation - Scopus: 50
    Optical Solitons, Nonlinear Self-Adjointness and Conservation Laws for Kundu-Eckhaus Equation
    (Elsevier Science Bv, 2017) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru
    In this article, Kundu-Eckhaus equation (KE) is studied from the perspective of modified tanhcoth method (MTC), extended Jacobi elliptic function expansion method (EJEF), Lie symmetry analysis, nonlinear self-adjointness and conservation laws (Cls). New soliton solutions like combined dark-bright, dark, periodic wave and singular soliton solutions are obtained. The equation is found to be a nonlinear self-adjoint, we construct the Cls using the new conservation theorem presented by Ibragimov. Physical interpretation for some of the obtained solutions are illustrated in Figures.
  • 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.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 24
    Optimal System, Nonlinear Self-Adjointness and Conservation Laws for Generalized Shallow Water Wave Equation
    (de Gruyter Poland Sp Zoo, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru
    In this article, the generalized shallow water wave (GSWW) equation is studied from the perspective of one dimensional optimal systems and their conservation laws (Cls). Some reduction and a new exact solution are obtained from known solutions to one dimensional optimal systems. Some of the solutions obtained involve expressions with Bessel function and Airy function [1-3]. The GSWW is a nonlinear self-adjoint (NSA) with the suitable differential substitution, Cls are constructed using the new conservation theorem.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 42
    Space-Time Fractional Rosenou-Haynam Equation: Lie Symmetry Analysis, Explicit Solutions and Conservation Laws
    (Springeropen, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru
    This article uses the extension of the Lie symmetry analysis (LSA) and conservation laws (Cls) (Singla et al. in Nonlinear Dyn. 89(1):321-331, 2017; Singla et al. in J. Math. Phys. 58: 051503, 2017) for the space-time fractional partial differential equations (STFPDEs) to analyze the space-time fractional Rosenou-Haynam equation (STFRHE) with Riemann-Liouville (RL) derivative. We transform the space-time fractional RHE to a nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries. The reduced equation's derivative is in Erdelyi-Kober (EK) sense. We use the power series (PS) technique to derive explicit solutions for the reduced ODE for the first time. The Cls for the governing equation are constructed using a new conservation theorem.
  • Article
    Citation - WoS: 24
    Citation - Scopus: 26
    Conservation Laws, Soliton-Like and Stability Analysis for the Time Fractional Dispersive Long-Wave Equation
    (Springeropen, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi
    In this manuscript we investigate the time fractional dispersive long wave equation (DLWE) and its corresponding integer order DLWE. The symmetry properties and reductions are derived. We construct the conservation laws (Cls) with Riemann-Liouville (RL) for the time fractional DLWE via a new conservation theorem. The conformable derivative is employed to establish soliton-like solutions for the governing equation by using the generalized projective method (GPM). Moreover, the Cls via the multiplier technique and the stability analysis via the concept of linear stability analysis for the integer order DLWE are established. Some graphical features are presented to explain the physical mechanism of the solutions.