Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article On Optical Solitons of the Non-Local Nlse With Time Dependent Coefficients(Natl inst Optoelectronics, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Kilic, Bulent; Inc, Mustafa; MatematikThis paper integrates non-local nonlinear Schrodinger equation (NNLSE) with time dependent coefficients. The first integral method (FIM) is applied to report the optical soliton solutions of NNLSE with parabolic law nonlinearity and time dependent coefficients which are the terms of velocity dipersion, linear and nonlinear terms and also non-local one.Article Citation - WoS: 10Citation - Scopus: 9Bright, Dark, and Singular Optical Soliton Solutions for Perturbed Gerdjikov-Ivanov Equation(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Kumar, Sunil; Ulutas, Esma; Mustafa, I.N.C.This study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this equation that models pulse dynamics in optical fibers. It is retrieved some bright, dark optical and singular solitons profile in the limiting cases of the Jacobi elliptic functions. The constraint conditions depending on the parameters for the existence of solitons are also presented.Article Citation - WoS: 8Citation - Scopus: 8Dynamical Behaviour of the Joseph-Egri Equation(Vinca inst Nuclear Sci, 2023) Inc, Mustafa; Leta, Temesgen D.; Baleanu, Dumitru; Rezazade, Hadi; Sabi'u, Jamilu; Rezazadeh, Hadi; Sabi’u, JamiluWe investigate traveling wave solutions to the Joseph-Egri equation via extended auxiliary equation technique. We have determined stationary points of the dynamical systems by using bifurcation method. We also acquire cusp, periodic and homoclinic orbits. The investigated solutions are entirely different from the reported in the liter-ature. However, some of the reported solutions are plotted to understand the physical application of the considered model using renowned mathematical software.Article Citation - WoS: 13Citation - Scopus: 15N-Wave and Other Solutions To the B-Type Kadomtsev-Petviashvili Equation(Vinca inst Nuclear Sci, 2019) Hosseini, Kamyar; Samavat, Majid; Mirzazadeh, Mohammad; Eslami, Mostafa; Moradi, Mojtaba; Baleanu, Dumitru; Inc, MustafaThe present article studies a B-type Kadomtsev-Petviashvili equation with certain applications in the fluids. Stating with the Hirota's bilinear form and adopting reliable methodologies, a group of exact solutions such as the N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation is formally derived. Some figures in two and three dimensions are given to illustrate the characteristics of the obtained solutions. The results of the current work actually help to complete the previous studies about the B-type Kadomtsev-Petviashvili equation.Article Citation - WoS: 17Citation - Scopus: 17Yficitious Time Integration Method for Solving the Time Fractional Gas Dynamics Equation(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Baleanu, Dumitru; Moshokoa, Seithuti Philemon; Partohaghighi, MohammadIn 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.Article Citation - WoS: 21Citation - Scopus: 23Optical Solitons, Conservation Laws and Modulation Instability Analysis for the Modified Nonlinear Schrodinger's Equation for Davydov Solitons(Taylor & Francis Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaIn this paper, the optical solitons to the modified nonlinear Schrodinger's equation for davydov solitons are investigate. The modified F-expansion method is the integration technique employed to achieve this task. This yielded a combined and other soliton solutions. The Lie point symmetry generators of a system of partial differential equations acquired by decomposing the equation into real and imaginary components 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 local conservation laws (Cls) for the system using the general Cls theorem presented by Ibragimov. Furthermore, the modulation instability (MI) is analyzed 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.Article Citation - WoS: 7Citation - Scopus: 6Grey and Black Optical Solitary Waves, and Modulation Instability Analysis To the Perturbed Nonlinear Schrodinger Equation With Kerr Law Nonlinearity(Taylor & Francis Ltd, 2019) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaThis paper addresses the nonlinear Schrodinger equation (NLSE) with Kerr law nonlinearity and perturbation terms in optical fibre. A class of grey and black optical solitary wave solutions of this equation are retrieved by adopting an appropriate solitary wave ansatz solution. These types of solitary waves play a vital role in understanding various physical phenomena in nonlinear systems. This lead to a constraint condition on the solitary wave parameters which must hold for the solitary waves to exist. Moreover, the modulation instability (MI) analysis of the model is studied by employing the concept of linear-stability analysis (LSA) 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 behaviours of the equation.Article Citation - WoS: 3Citation - Scopus: 7On Exact Solutions for New Coupled Non-Linear Models Getting Evolution of Curves in Galilean Space(Vinca inst Nuclear Sci, 2019) Cavlak Aslan, Ebru; Inc, Mustafa; Baleanu, Dumitru; Kucukarslan Yuzbasi, ZuhalIn this work, the new coupled non-linear partial differential equations (CNLPDE) getting the time evolution of the curvatures of the evolving curve are derived in the Galilean space. Exact solutions for these new CNLPDE are obtained Finally, Lie symmetry analysis is performed on these new CNLPDE and the algebra of Lie point symmetries of these new equations is found.Article Citation - WoS: 3Citation - Scopus: 6Adomian-Pade Approximate Solutions To the Conformable Non-Linear Heat Transfer Equation(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaThis paper adopts the Adomian decomposition method and the Pade approximation technique to derive the approximate solutions of a conformable heat transfer equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing the approximate solutions.Article Citation - WoS: 22Citation - Scopus: 23Modified Variational Iteration Method for Straight Fins With Temperature Dependent Thermal Conductivity(Vinca inst Nuclear Sci, 2018) Khan, Hasib; Baleanu, Dumitru; Khan, Aziz; Inc, MustafaThe modified variational iteration method (MVIM) has been used to calculate the efficiency of straight fins with temperature dependent thermal conductivity. The obtained results are compared with homotopy analysis method (HAM), homotopy perturbation method (HPM), and Adomian decomposition method (ADM). It is used w # 0 auxiliary parameter to keep under control convergence region of solution series in MVIM. As a result, although MVIM and HAM give results close to each other; HPM and ADM give divergent results from analytical solution.