Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article 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: 21Citation - Scopus: 20Single and Combined Optical Solitons, and Conservation Laws in (2+1)-Dimensions With Kundu-Mukherjee Equation(Elsevier, 2020) Li, Yongjin; Baleanu, Dumitru; Aliyu, Aliyu IsaIn this work, the celebrated (2 + 1)-dimensional Kundu-Mukherjee-Naskar equation (KMNE) proposed to govern the soliton dynamics in (2 + 1)-dimensions along excited resonant wave guides that is doped with Erbium atoms is studied with the aid of ansatz approach and sine-Gordon expansion method (SGEM). The integration algorithms revealed both single and combined optical solitons of the model. These solitons are reported as bright, dark, combined dark-bright and singular solitons. The combined dark-bright and combined singular soliton solutions of the KMNE are to the best of our knowledge reported for the first time in this paper. These solutions supplements the existing ones in the literature. Additionally, we studied the conservation laws (Cls) of the equation by applying the multipliers approach and report the non-trivial fluxes associated with the equation. 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 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.