Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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 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 Improved (G'/G)-expansion method for the time-fractional biological population model and Cahn-Hilliard equation(ASME, 2015) Baleanu, Dumitru; Uǧurlu, Yavuz; İnç, Mustafa; Kılıç, BülentIn this paper, we used improved (G'/G)-expansion method to reach the solutions for some nonlinear time-fractional partial differential equations (fPDE). The fPDE is reduced to an ordinary differential equation (ODE) by means of Riemann-Liouille derivative and a basic variable transformation. Various types of functions are obtained for the time-fractional biological population model (fBPM) and Cahn-Hilliard (fCH) equation. Copyright © 2015 by ASME.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 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 Optical solitons and modulation instability analysis with (3+1)-dimensional nonlinear Shrodinger equation(Academic Press LTD- Elsevier Science LTD, 2017) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, DumitruThis paper addresses the (3 + 1)-dimensional nonlinear Shrodinger equation (NLSE) that serves as the model to study the propagation of optical solitons through nonlinear optical fibers. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the solitary wave ansatz with Jaccobi elliptic function methods, we present the exact dark, bright and dark-bright or combined optical solitons to the model. The intensity as well as the nonlinear phase shift of the solitons are reported. The modulation instability aspects are discussed using the concept of linear stability analysis. The MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.