Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 10 of 26
  • 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, Ilyas
  • Article
    Citation - Scopus: 10
    The 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. © 2022
  • Article
    Citation - WoS: 26
    Citation - Scopus: 26
    The 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
    Citation - WoS: 27
    Citation - Scopus: 28
    Symmetry 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, Shrouk
    In 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: 21
    Citation - Scopus: 20
    Single and Combined Optical Solitons, and Conservation Laws in (2+1)-Dimensions With Kundu-Mukherjee Equation
    (Elsevier, 2020) Li, Yongjin; Baleanu, Dumitru; Aliyu, Aliyu Isa
    In 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
    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, Dumitru
    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.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 15
    Lump, Its Interaction Phenomena and Conservation Laws To a Nonlinear Mathematical Model
    (Elsevier, 2022) Sulaiman, Tukur Abdulkadir; Hincal, Evren; Baleanu, Dumitru; Yusuf, Abdullahi
    We 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: 30
    Citation - Scopus: 44
    Lie 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, Adil
    In 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: 38
    Citation - Scopus: 39
    Combined Optical Solitary Waves and Conservation Laws For. Nonlinear Chen-Lee Equation in Optical Fibers
    (Elsevier Gmbh, Urban & Fischer verlag, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    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.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 9
    A 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, Dumitru
    In 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.