Browsing by Author "İnç, Mustafa"

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Combined Optical Solitary Waves and Conservation Laws For Nonlinear Chen-Lee-Liu Equation in Optical Fibers
(Elsevier GMBH, Urban & Fischer Verlag, 2018) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389; Matematik
This 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.
Dark-bright optical solitary waves and modulation instability analysis with (2+1)-dimensional cubic-quintic nonlinear Schrodinger equation
(Taylor&Francis LTD, 2019) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389; Matematik
This paper addresses the (2+1)-dimensional cubic-quintic nonlinear Schrodinger equation (CQNLS) that serves as the model to study the light propagation through nonlinear optical media and non-Kerr crystals. A dark-bright optical solitary wave solution of this equation is retrieved by adopting the complex envelope function ansatz. This type of solitary wave describes the properties of bright and dark optical solitary waves in the same expression. The integration naturally lead to a constraint condition placed on the solitary wave parameters which must hold for the solitary waves to exist. Additionally, the modulation instability (MI) analysis of the model is studied based on the standard linear stability analysis and the MI gain spectrum is got. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CQNLS.
Dynamics of optical solitons, multipliers and conservation laws to the nonlinear schrodinger equation in (2+1)-dimensions with non-Kerr law nonlinearity
(2019) Baleanu, Dumitru; Tchier, Fairouz; İnç, Mustafa; Yusuf, Abdullah; Baleanu, Dumitru; 56389; Matematik
This 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.
Improved (G'/G)-expansion method for the time-fractional biological population model and Cahn-Hilliard equation
(2015) Baleanu, Dumitru; Uǧurlu, Yavuz; İnç, Mustafa; Kılıç, Bülent; 56389; Matematik
In 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.
Invariant subspaces, exact solutions and classification of conservation laws for a coupled (1+1)-dimensional nonlinear Wu-Zhang equation
(2020) Baleanu, Dumitru; Li, Yongjin; İnç, Mustafa; Baleanu, Dumitru; 56389; Matematik
In 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.
On new traveling wave solutions of potential KdV and (3+1)-dimensional Burgers equations
(Int Scientific Research Publications, 2016) Baleanu, Dumitru; İnan, İbrahim E.; Uğurlu, Yavuz; İnç, Mustafa; Baleanu, Dumitru; 56389; Matematik
This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables (G'/G, 1/G) expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena. (C) 2016 All rights reserved.
Optical solitary waves and conservation laws to the (2+1)-dimensional hyperbolic nonlinear Schrodinger equation
(2018) Baleanu, Dumitru; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389; Matematik
This 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.
Optical Solitary Waves And Conservation Laws To The (2+1)-Dimensional Hyperbolic Nonlinear Schrodinger Equation
(World Scientific Publ CO PTE LTD, 2018) Baleanu, Dumitru; İnç, Mustafa; Yusuf, A.; Baleanu, Dumitru; 56389; Matematik
This 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.
Optical solitons and modulation instability analysis of an integrable model of (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation
(2017) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389; Matematik
This paper addresses the nonlinear Schrbdinger type equation (NLSE) in (2+1)-dimensions which describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) with anisotropic and bilinear interactions in the semiclassical limit. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the generalized tanh methods. Dark, dark-bright or combined optical and singular soliton solutions of the equation are derived. Furthermore, the modulational instability (MI) is studied based on the standard linear-stability analysis and the MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier Ltd. All rights reserved.
Optical Solitons And Modulation Instability Analysis of an Integrable Model of (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation
(Academic Press LTD- Elsevier Science LTD, 2017) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389; Matematik
This paper addresses the nonlinear Schrbdinger type equation (NLSE) in (2+1)-dimensions which describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) with anisotropic and bilinear interactions in the semiclassical limit. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the generalized tanh methods. Dark, dark-bright or combined optical and singular soliton solutions of the equation are derived. Furthermore, the modulational instability (MI) is studied based on the standard linear-stability analysis and the MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier Ltd. All rights reserved.
Optical solitons and modulation instability analysis with (3+1)-dimensional nonlinear Shrodinger equation
(Academic Press LTD- Elsevier Science LTD, 2017) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389; Matematik
This 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.
Optical solitons to the (n+1)-dimensional nonlinear Schrodinger's equation with Kerr law and power law nonlinearities using two integration schemes
(2019) Baleanu, Dumitru; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru; 56389; Matematik
In 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.
Solitons and complexitons to the (2+1)-dimensional Heisenberg ferromagnetic spin chain model
(2019) Baleanu, Dumitru; Li, Yongjin; İnç, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; 56389; Matematik
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.
Solitons and Conservation Laws for the (2+1)-Dimensional Davey-Stewartson Equations with Conformable Derivative
(2018) Baleanu, Dumitru; İnç, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; 56389; Matematik
This research obtains some new solitons for the Davey-Stewartson equation (DSE) with conformable derivative. The well known projective Ricatti equation ansatz (PREA) is employed to reach such solitons. The constraints conditions for the existence of soliton solutions are reported. Moreover, the conservation laws (Cls) for the governing equation is studied via multiplier technique. Physical features of some solutions are illustrated in Figures 1-8.
The first integral method for the (3+1)-dimensional modified korteweg-de vries-zakharov-kuznetsov and hirota equations
(Editura Academiei Romane, 2015) Baleanu, Dumitru; Kılıç, B.; Uğurlu, Y.; İnç, Mustafa; Matematik
The first integral method is applied to get the different types of solutions of the (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and Hirota equations. We obtain envelope, bell shaped, trigonometric, and kink soliton solutions of these nonlinear evolution equations. The applied method is an effective one to obtain different types of solutions of nonlinear partial differential equations
YFICITIOUS TIME INTEGRATION METHOD FOR SOLVING THE TIME FRACTIONAL GAS DYNAMICS EQUATION
(2019) Baleanu, Dumitru; İnç, Mustafa; Baleanu, Dumitru; Moshokoa, Seithuti Philemon; 56389; Matematik
In this work a poweful approach is presented to solve the time-fractional gas dynamics equation. In fact, we use a fictitious time variable y to convert the dependent variable w(x, t) into a new one with one more dimension. Then by taking a initial guess and implementing the group preserving scheme we solve the problem. Finally four examples are solved to illustrate the power of the offered method.