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: 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 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) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, DumitruIn 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.Article Solitons and complexitons to the (2+1)-dimensional Heisenberg ferromagnetic spin chain model(World Scientific Publ Co Pte Ltd, 2019) Aliyu, Aliyu Isa; Li, Yongjin; İnç, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.This 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: 51Citation - Scopus: 56Optical Solitons for Complex Ginzburg-Landau Model in Nonlinear Optics(Elsevier Gmbh, Urban & Fischer verlag, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaThis paper studies the complex Ginzburg-Landau equation (CGLE) which models soliton propagation in the presence of detuning factor in nonlinear optics. Dark, bright, dark-singular and a new dark-bright optical soliton solutions to the model are derived using the sine-Gordon equation method (SGEM). Singular soliton solutions are also celebrated. The model is studied with Kerr law, quadratic-cubic law and parabolic laws nonlinear fibers. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CGLE. (C) 2017 Elsevier GmbH. All rights reserved.Article Citation - WoS: 40Citation - Scopus: 48Dispersive Optical Solitons and Modulation Instability Analysis of Schrodinger-Hirota Equation With Spatio-Temporal Dispersion and Kerr Law Nonlinearity(Academic Press Ltd- Elsevier Science Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaThis paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the perturbed nonlinear Schrodinger-Hirota equation (SHE) with spatio-temporal dispersion (STD) and Kerr law nonlinearity in optical fibers. The integration algorithm is the Sine-Gordon equation method (SGEM). Furthermore, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis and the MI gain spectrum is got. (C) 2017 Elsevier Ltd. All rights reserved.Article Citation - WoS: 46Citation - Scopus: 49Optical Solitons To the Resonance Nonlinear Schrodinger Equation by Sine-Gordon Equation Method(Academic Press Ltd- Elsevier Science Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaIn this paper, we examined the optical solitons to the resonant nonlinear Schrodinger equation (R-NLSE) which describes the propagation of solitons through optical fibers. Three types of nonlinear media fibers are studied. They are; quadratic-cubic law, Kerr law and parabolic law. Dark, bright, dark-bright or combined optical and singular soliton solutions are derived using the sine-Gordon equation method (SGEM). The constraint conditions that naturally fall out of the solution structure which guarantee the existence of these solitons are also reported. (C) 2017 Elsevier Ltd. All rights reserved.Article Citation - WoS: 44Citation - Scopus: 49Optical Solitons for Biswas-Milovic Model in Nonlinear Optics by Sine-Gordon Equation Method(Elsevier Gmbh, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaThis article studies the dynamics of optical solitons to the Biswas-Milovic equation (BME) which describes the dynamics of optical solitons in generalized form. There are four types of nonlinear fibers studied in this paper. They are quadratic-cubic, Kerr and Parabolic laws. The integration algorithm adopted is the Sine-Gordon equation method (SGEM). Dark, bright and dark-singular optical solitons are derived. Complex singular solitons are also reported. The obtained results have important applications in the study of solitons in optical fibers. (C) 2017 Elsevier GmbH. All rights reserved.Article Citation - WoS: 11Citation - Scopus: 12Optical Solitons and Stability Analysis in Ring-Cavity Fiber System With Carbon Nanotube as Saturable Absorber(Iop Publishing Ltd, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaThis paper addresses the ring-cavity fiber laser system. A class of gray and black soliton solutions of the model are reported by adopting an appropriate envelope ansatz. Further more, the modulation instability (MI) of the equation is studied using the linear-stability analysis (LSA) technique and the MI gain spectrum is derived. 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.