WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Subject: search.filters.subject.ClsWoS Q: search.filters.wosQuartile.Q2

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Now showing 1 - 4 of 4
  • 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: 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: 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.