Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 7Citation - Scopus: 9Solitons and Complexitons To the (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Model(World Scientific Publ Co Pte Ltd, 2019) Li, Yongjin; Inc, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; Aliyu, Aliyu IsaThis paper investigates the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain (HMF) model. The model describes the nonlinear spin dynamics of HMF. By adopting the modified F-Expansion and projective Riccati equation methods, we report the dark, combined dark-bright and envelope optical solitons, complexitons singular solutions of the equation along with the conditions that must be satisfied for solitons to exist. 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: 32Citation - Scopus: 35Complexiton and Solitary Wave Solutions of the Coupled Nonlinear Maccaris System Using Two Integration Schemes(World Scientific Publ Co Pte Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Nuray, Elif; Inc, MustafaIn this paper, we consider a coupled nonlinear Maccaris system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.Article Citation - WoS: 15Citation - Scopus: 21On the Classification of Conservation Laws and Soliton Solutions of the Long Short-Wave Interaction System(World Scientific Publ Co Pte Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaIn this paper, the classification of conservation laws (Cis) of the long short-wave interaction system (LSWS) which appears in fluid mechanics as well as plasma physics is implemented using two Cls theorems, namely, the multipliers approach and the new conservation theorem. The LSWS describes the interaction between one long longitudinal wave and one short transverse wave propagating in a generalized elastic medium. The zeroth-order multipliers and the nonlinear self-adjoint substitutions of the model are derived. Considering the fact that the new conservation theorem needs Lie point symmetries in constructing Cls, we derive the point symmetries of a system of nonlinear partial differential equations (NPDEs) acquired by transforming the model into real and imaginary components. Moreover, we derive some kink-type, bell-shaped, singular and combined soliton solutions to the model using the powerful sine-Gordon expansion method (SGEM). Some figures are presented to show the physical interpretations of the acquired results.Article Citation - WoS: 17Citation - Scopus: 19Optical Solitary Waves and Conservation Laws To the (2+1)-Dimensional Hyperbolic Nonlinear Schrodinger Equation(World Scientific Publ Co Pte Ltd, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaThis work studies the hyperbolic nonlinear Schrodinger equation (H-NLSE) in (2 + 1)-dimensions. The model describes the evolution of the elevation of water wave surface for slowly modulated wave trains in deep water in hydrodynamics, and also governs the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics. A class of gray and black optical solitary wave solutions of the H-NLSE are reported by adopting an appropriate solitary wave ansatz solution. Moreover, classification of conservation laws (Cls) to the H-NLSE is implemented using the multipliers approach. Some physical interpretations and analysis of the results obtained are also presented.Article Citation - WoS: 9Citation - Scopus: 12Symmetry Reductions, Explicit Solutions, Convergence Analysis and Conservation Laws Via Multipliers Approach To the Chen-Lee Model in Nonlinear Optics(World Scientific Publ Co Pte Ltd, 2019) Inc, Mustafa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru; Aliyu, Aliyu IsaIn this paper, symmetry analysis is performed for the nonlinear Chen-Lee-Liu equation (NCLE) arising in temporal pulses. New forms of explicit solutions of the equation are constructed using the optimal systems by applying the power series solutions (PSS) technique and the convergence of the PSS is investigated. Finally, the conservation laws (Cls) of the model is studied using the multiplier approach.Article Citation - WoS: 11Citation - Scopus: 15Optical Solitons To the (n+1)-Dimensional Nonlinear Schrodinger's Equation With Kerr Law and Power Law Nonlinearities Using Two Integration Schemes(World Scientific Publ Co Pte Ltd, 2019) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru; Inc, MustafaIn this study, two integration techniques are employed to reach optical solitons to the (n + 1)-dimensional nonlinear Schrodinger's equation ((n + 1)-NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented.