Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 21Citation - Scopus: 20Single and Combined Optical Solitons, and Conservation Laws in (2+1)-Dimensions With Kundu-Mukherjee Equation(Elsevier, 2020) Li, Yongjin; Baleanu, Dumitru; Aliyu, Aliyu IsaIn 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 Optical solitary waves and conservation laws to the (2+1)-dimensional hyperbolic nonlinear Schrodinger equation(World Scientific Publ Co Pte Ltd, 2018) Aliyu, Aliyu Isa; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, DumitruThis 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: 38Citation - Scopus: 39Combined 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, MustafaThis 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: 3Citation - Scopus: 3Invariant 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, AliyuIn 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: 14Citation - Scopus: 15Gray 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, MustafaThis 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 Combined Optical Solitary Waves and Conservation Laws For Nonlinear Chen-Lee-Liu Equation in Optical Fibers(Elsevier GMBH, Urban & Fischer Verlag, 2018) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, DumitruThis 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: 50Citation - Scopus: 51Optical 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, MustafaIn 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: 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: 25Citation - Scopus: 24Dynamics 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, MustafaThis 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.