Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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: 13Citation - Scopus: 16Optical and Singular Solitary Waves To the Pnlse With Third Order Dispersion in Kerr Media Via Two Integration Approaches(Elsevier Gmbh, Urban & Fischer verlag, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaIn this paper, the sine-Gordon expansion method (SGEM) and the generalized tanh (GTM) methods are employed to find the optical solitary wave solutions to the perturbed nonlinear Schrodinger equation (PNLSE) with Kerr law nonlinearity describing the propagation of optical solitary waves in nonlinear optical fibers. The dark, bright, dark-bright and dark-singular optical solitary waves are retrieved. Additionally, singular solitary waves are also derived as by-products of the integration scheme. Physical interpretations of the obtained results are demonstrated with interesting figures. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNLSE. (C) 2018 Elsevier GmbH. All rights reserved.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: 19Citation - Scopus: 18Optical Solitons for the Kundu-Eckhaus Equation With Time Dependent Coefficient(Elsevier Gmbh, Urban & Fischer verlag, 2018) Baleanu, Dumitru; Inc, MustafaThe first integral method (FIM) is applied to get the different type optical solitons of Kundu-Eckhaus equation (KE). A class of optical solitons of this equation is presented, and some of which are acquired for the first time. Constraint conditions guarantees existence of these solitons. It is illustrated that FIM is very effective method to reach the various type of the soliton solutions. (C) 2018 Elsevier GmbH. All rights reserved.Article Citation - WoS: 29Citation - Scopus: 29Optical Solitons of Transmission Equation of Ultra-Short Optical Pulse in Parabolic Law Media With the Aid of Backlund Transformation(Elsevier Gmbh, Urban & Fischer verlag, 2017) Baleanu, Dumitru; Inc, Mustafa; Al Qurashi, Maysaa' MohamedThe Backlund transformation is used to obtain optical soliton for a type of the Schrodinger equation. Kink-type and dark-optical soliton solutions are acquired of the Schrodinger equation. It is illustrated that the examined equation is integrable because if an equation has a Backlund transformation it could be integrable. Several constraint conditions for the parameters are derived that establish the existence of the soliton solutions. The numerical simulations supplement the analytical schemes. (C) 2017 Elsevier GmbH. All rights reserved.Article Citation - WoS: 51Citation - Scopus: 53New Solitary Wave Solutions and Conservation Laws To the Kudryashov-Sinelshchikov Equation(Elsevier Gmbh, Urban & Fischer verlag, 2017) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaIn this manuscript, we utilized the algorithm of Riccati Bernoulli sub-ODE method to find new soliton solutions to the Kudryashov Sinelshchikov equation (KSE). Some new type of traveling wave solutions are acquired, which includes the kink-type, singular-type and exponential function solutions which have not been obtained in previous time using this technique. The obtained solutions appear with all necessary constraint conditions that are necessary for them to exist. Using the general conservation laws (Cls) theorem introduced by Ibragimov, the Cls for the underlying equation are investigated. (C) 2017 Elsevier GmbH. All rights reserved.