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.Q3

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Now showing 1 - 9 of 9
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Lump-Type and Bell-Shaped Soliton Solutions of the Time-Dependent Coefficient Kadomtsev-Petviashvili Equation
    (Frontiers Media Sa, 2020) Li, Yongjin; Qi, Liu; Inc, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; Aliyu, Aliyu Isa
    In this article, the lump-type solutions of the new integrable time-dependent coefficient (2+1)-dimensional Kadomtsev-Petviashvili equation are investigated by applying the Hirota bilinear technique and a suitable ansatz. The equation is applied in the modeling of propagation of small-amplitude surface waves in large channels or straits of slowly varying width, depth and non-vanishing vorticity. Applying the Bell's polynomials approach, we successfully acquire the bilinear form of the equation. We firstly find a general form of quadratic function solution of the bilinear form and then expand it as the sums of squares of linear functions satisfying some conditions. Most importantly, we acquire two lump-type and a bell-shaped soliton solutions of the equation. To our knowledge, the lump type solutions of the equation are reported for the first time in this paper. The physical interpretation of the results are discussed and represented graphically.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Invariant Subspaces, Exact Solutions and Classification of Conservation Laws for a Coupled (1+1)-Dimensional Nonlinear Wu-Zhang Equation
    (Iop Publishing Ltd, 2020) Li, Yongjin; Inc, Mustafa; Baleanu, Dumitru; Aliyu, Aliyu Isa; Isa Aliyu, Aliyu
    In this work, we apply the invariant subspace method to derive a set of invariant subspaces and solutions of the nonlinear Wu-Zhang equation which describes the dynamic behavior of dispersive long waves in fluid dynamics. The method gives logarithmic and polynomial solutions of the equation. Furthermore, the multipliers approach and new conservation theorem are employed to derive a set of conservation laws of the equation which are to the best of our knowledge reported for the first time in this work. The physical structure of the results is shown by figures of some special solutions in order to give us a better interpretation on the evolution of the solutions.
  • Article
    Citation - WoS: 36
    Citation - Scopus: 35
    Traveling Wave Solutions and Conservation Laws for Nonlinear Evolution Equation
    (Amer inst Physics, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru
    In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated. Published by AIP Publishing.
  • 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: 25
    Citation - Scopus: 24
    Dynamics of Optical Solitons, Multipliers and Conservation Laws To the Nonlinear Schrodinger Equation in (2+1)-Dimensions With Non-Kerr Law Nonlinearity
    (Taylor & Francis Ltd, 2019) Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa; Tchier, Fairouz; Inc, Mustafa
    This work studies the (2 + 1)-dimensional nonlinear Schrodinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 6
    Grey and Black Optical Solitary Waves, and Modulation Instability Analysis To the Perturbed Nonlinear Schrodinger Equation With Kerr Law Nonlinearity
    (Taylor & Francis Ltd, 2019) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    This paper addresses the nonlinear Schrodinger equation (NLSE) with Kerr law nonlinearity and perturbation terms in optical fibre. A class of grey and black optical solitary wave solutions of this equation are retrieved by adopting an appropriate solitary wave ansatz solution. These types of solitary waves play a vital role in understanding various physical phenomena in nonlinear systems. This lead to a constraint condition on the solitary wave parameters which must hold for the solitary waves to exist. Moreover, the modulation instability (MI) analysis of the model is studied by employing the concept of linear-stability analysis (LSA) 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 behaviours of the equation.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 6
    Adomian-Pade Approximate Solutions To the Conformable Non-Linear Heat Transfer Equation
    (Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
    This paper adopts the Adomian decomposition method and the Pade approximation technique to derive the approximate solutions of a conformable heat transfer equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing the approximate solutions.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Approximate Solutions and Conservation Laws of the Periodic Base Temperature of Convective Longitudinal Fins in Thermal Conductivity
    (Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
    In this paper, the residual power series method is used to study the numerical approximations of a model of oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. It is shown that the residual power series method is efficient for examining numerical behavior of non-linear models. Further, the conservation of heat is studied using the multiplier method.
  • Article
    Citation - WoS: 88
    Citation - Scopus: 94
    Optical Solitons Possessing Beta Derivative of the Chen-Lee Equation in Optical Fibers
    (Frontiers Media Sa, 2019) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi
    This research obtains some new optical soliton solutions with beta derivative for Chen-Lee-Liu equation (CLL) in optical fibers. Three integration schemes which are Ricatti-Bernoulli (RB) sub-ODE, generalized Bernoulli (GB) sub-ODE and generalized tanh (GT) methods are applied to reach such solutions. The constraints conditions for the existence of soliton solutions are reported. The solutions are obtained using newly introduced fractional derivative called beta derivative. Numerical simulations of some of the obtained solutions are illustrated.