WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 26Citation - Scopus: 26The Geophysical Kdv Equation: Its Solitons, Complexiton, and Conservation Laws(Springer Heidelberg, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; Mirzazadeh, M.; Akinyemi, L.The main goal of the current paper is to analyze the impact of the Coriolis parameter on nonlinear waves by studying the geophysical KdV equation. More precisely, specific transformations are first adopted to derive one-dimensional and operator forms of the governing model. Solitons and complexiton of the geophysical KdV equation are then retrieved with the help of several well-established approaches such as the Kudryashov and Hirota methods. In the end, the new conservation theorem given by Ibragimov is formally employed to extract conservation laws of the governing model. It is shown that by increasing the Coriolis parameter, based on the selected parameter regimes, less time is needed for tending the free surface elevation to zero.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 Citation - WoS: 26Citation - Scopus: 36Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of a Spatially Two-Dimensional Burgers-Huxley Equation(Mdpi, 2020) Bano, Shahida; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Hussain, AmjadIn this paper, we investigate a spatially two-dimensional Burgers-Huxley equation that depicts the interaction between convection effects, diffusion transport, reaction gadget, nerve proliferation in neurophysics, as well as motion in liquid crystals. We have used the Lie symmetry method to study the vector fields, optimal systems of first order, symmetry reductions, and exact solutions. Furthermore, using the power series method, a set of series solutions are obtained. Finally, conservation laws are derived using optimal systems.Article Citation - WoS: 15Citation - Scopus: 21On the Classification of Conservation Laws and Soliton Solutions of the Long Short-Wave Interaction System(World Scientific Publ Co Pte Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaIn this paper, the classification of conservation laws (Cis) of the long short-wave interaction system (LSWS) which appears in fluid mechanics as well as plasma physics is implemented using two Cls theorems, namely, the multipliers approach and the new conservation theorem. The LSWS describes the interaction between one long longitudinal wave and one short transverse wave propagating in a generalized elastic medium. The zeroth-order multipliers and the nonlinear self-adjoint substitutions of the model are derived. Considering the fact that the new conservation theorem needs Lie point symmetries in constructing Cls, we derive the point symmetries of a system of nonlinear partial differential equations (NPDEs) acquired by transforming the model into real and imaginary components. Moreover, we derive some kink-type, bell-shaped, singular and combined soliton solutions to the model using the powerful sine-Gordon expansion method (SGEM). Some figures are presented to show the physical interpretations of the acquired results.Article Citation - WoS: 17Citation - Scopus: 19Optical Solitary Waves and Conservation Laws To the (2+1)-Dimensional Hyperbolic Nonlinear Schrodinger Equation(World Scientific Publ Co Pte Ltd, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaThis 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 Citation - WoS: 9Citation - Scopus: 12Symmetry Reductions, Explicit Solutions, Convergence Analysis and Conservation Laws Via Multipliers Approach To the Chen-Lee Model in Nonlinear Optics(World Scientific Publ Co Pte Ltd, 2019) Inc, Mustafa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru; Aliyu, Aliyu IsaIn this paper, symmetry analysis is performed for the nonlinear Chen-Lee-Liu equation (NCLE) arising in temporal pulses. New forms of explicit solutions of the equation are constructed using the optimal systems by applying the power series solutions (PSS) technique and the convergence of the PSS is investigated. Finally, the conservation laws (Cls) of the model is studied using the multiplier approach.Article Citation - WoS: 34Citation - Scopus: 39Lie Symmetry Analysis and Conservation Laws for the Time Fractional Simplified Modified Kawahara Equation(Sciendo, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, DumitruIn this work, Lie symmetry analysis for the time fractional simplified modified Kawahara (SMK) equation with Riemann-Liouville (RL) derivative, is analyzed. We transform the time fractional SMK equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in the Erdelyi-Kober (EK) sense. We solve the reduced fractional ODE using a power series technique. Using Ibragimov's nonlocal conservation method to time fractional partial differential equations, we compute conservation laws (Cls) for the time fractional SMK equation. Some figures of the obtained explicit solution are presented.Article Citation - WoS: 39Citation - Scopus: 42Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Sixth-Order Nonlinear Ramani Equation(Mdpi, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaIn this work, we study the completely integrable sixth-order nonlinear Ramani equation. By applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system of one-dimensional sub-algebras of the equation are derived. The optimal system is further used to derive the symmetry reductions and exact solutions. In conjunction with the Riccati Bernoulli sub-ODE (RBSO), we construct the travelling wave solutions of the equation by solving the ordinary differential equations (ODEs) obtained from the symmetry reduction. We show that the equation is nonlinearly self-adjoint and construct the conservation laws (CL) associated with the Lie symmetries by invoking the conservation theorem due to Ibragimov. Some figures are shown to show the physical interpretations of the acquired results.