Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of a Spatially Two-Dimensional Burgers-Huxley Equation(MDPI AG, 2020) Bano, Shahida; Baleanu, Dumitru; Hussain, Amjad; Nisar, Kottakkaran Sooppy; Khan, IlyasArticle Citation - Scopus: 10The Korteweg-De Vries–caudrey–dodd–gibbon Dynamical Model: Its Conservation Laws, Solitons, and Complexiton(Shanghai Jiaotong University, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; Mirzazadeh, M.; Dehingia, K.The main purpose of the present paper is to conduct a detailed and thorough study on the Korteweg-de Vries–Caudrey–Dodd–Gibbon (KdV-CDG) dynamical model. More precisely, after considering the integrable KdV-CDG dynamical model describing certain properties of ocean dynamics, its conservation laws, solitons, and complexiton are respectively derived using the Ibragimov, Kudryashov, and Hirota methods. Several numerical simulations in two and three-dimensional postures are formally given to analyze the effect of nonlinear parameters. It is shown that nonlinear parameters play a key role in the dynamical properties of soliton and complexiton solutions. © 2022Article Citation - WoS: 27Citation - Scopus: 28Symmetry Reduction, Conservation Laws and Acoustic Wave Solutions for the Extended Zakharov-Kuznetsov Dynamical Model Arising in a Dust Plasma(Elsevier, 2020) Seadawy, Aly R.; EL-Kalaawy, O. H.; Maowad, S. M.; Baleanu, Dumitru; Wael, ShroukIn this article, we consider the extended Zakharov-Kuznetsov (EZK) equation, which describes the nonlinear plasma dust acoustic waves (DAWs) in a magnetized dusty plasma. Dusty plasmas consist of three components: electrons, highly negatively charged dust grains, and two-temperature ions (low-temperature ions and high temperature ions). We study the Lie symmetries, reductions, conservation laws and new exact solutions of EZK equations. Conservation laws for EZK equation is derived by applying the new conservation theorem of Ibragimov. Similarity solution for EZK equation will be obtained using Lie symmetry method. We find the Lie symmetries group of EZK equation, using similarity variables, get reduction equation, solving the reduction equations and then get the similarity solution. Solitary wave solutions of the EZK equation are derived from the reduction equation. Thus, some new exact explicit solutions of the EZK equation are obtained.Article Citation - WoS: 14Citation - Scopus: 15Lump, Its Interaction Phenomena and Conservation Laws To a Nonlinear Mathematical Model(Elsevier, 2022) Sulaiman, Tukur Abdulkadir; Hincal, Evren; Baleanu, Dumitru; Yusuf, AbdullahiWe solve the Ostrovsky equation in the absence of the rotation effect using the Hirota bilinear method and symbolic calculation. Some unique interaction phenomena have been obtained between lump so-lution, breather wave, periodic wave, kink soliton, and two-wave solutions. All the obtained solutions are validated by putting them into the original problem using the Wolfram Mathematica 12. The physical characteristics of the solutions have been visually represented to shed additional light on the acquired re-sults. Furthermore, using the novel conservation theory, the conserved vectors of the governing equation have been generated. The discovered results are helpful in understanding particular physical phenomena in fluid dynamics as well as the dynamics of nonlinear higher dimensional wave fields in computational physics and ocean engineering and related disciplines.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )Article Citation - WoS: 30Citation - Scopus: 44Lie Analysis, Conservation Laws and Travelling Wave Structures of Nonlinear Bogoyavlenskii-Kadomtsev Equation(Elsevier, 2020) Hussain, Amjad; Junaid-U-Rehman, M.; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Jhangeer, AdilIn this paper, the Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation is taken into consideration by means of Lie symmetry analysis. Infinitesimal generators are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Henceforth, conjugacy classes of abelian algebra are used to find the similarity reductions, which convert the considered equation into ordinary differential equations (ODEs). Further, these ODEs are taken into consideration, and travelling wave structures are computed by applying different techniques. Moreover, the discussed model is discussed by means of nonlinear selfadjointness and conservation laws are derived for each Lie symmetry generator. For specific values of the physical parameters of the equation under discussion, the graphical behaviour of some solutions is depicted.Article Citation - WoS: 5Citation - Scopus: 9A New Fourth-Order Integrable Nonlinear Equation: Breather, Rogue Waves, Other Lump Interaction Phenomena, and Conservation Laws(Springer, 2021) Alshomrani, Ali Saleh; Ullah, Malik Zaka; Baleanu, DumitruIn this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation such as the group of transformations, commutator and adjoint representation tables. A differential substitution is found by nonlinear self-adjointness (NSA) and thereafter the associated conservation laws are established. We show some dynamical characteristics of the obtained solutions through via the 3-dimensional and contour graphs.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: 2Citation - Scopus: 2Approximate Solutions and Conservation Laws of the Periodic Base Temperature of Convective Longitudinal Fins in Thermal Conductivity(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaIn this paper, the residual power series method is used to study the numerical approximations of a model of oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. It is shown that the residual power series method is efficient for examining numerical behavior of non-linear models. Further, the conservation of heat is studied using the multiplier method.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.