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Pinar, Zehra. (1400). The symmetry analysis and analytical studies of the rotational GreenNaghdi (R-GN) equation. سامانه مدیریت نشریات علمی, 9(4), 1223-1232. doi: 10.22034/cmde.2020.41145.1785
Zehra Pinar. "The symmetry analysis and analytical studies of the rotational GreenNaghdi (R-GN) equation". سامانه مدیریت نشریات علمی, 9, 4, 1400, 1223-1232. doi: 10.22034/cmde.2020.41145.1785
Pinar, Zehra. (1400). 'The symmetry analysis and analytical studies of the rotational GreenNaghdi (R-GN) equation', سامانه مدیریت نشریات علمی, 9(4), pp. 1223-1232. doi: 10.22034/cmde.2020.41145.1785
Pinar, Zehra. The symmetry analysis and analytical studies of the rotational GreenNaghdi (R-GN) equation. سامانه مدیریت نشریات علمی, 1400; 9(4): 1223-1232. doi: 10.22034/cmde.2020.41145.1785

The symmetry analysis and analytical studies of the rotational GreenNaghdi (R-GN) equation

Computational Methods for Differential Equations
مقاله 20، دوره 9، شماره 4، دی 2021، صفحه 1223-1232    اصل مقاله (240.13 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.41145.1785
نویسنده
Zehra Pinar*
Tekirdağ Namık Kemal University, Faculty of Arts and Science, Department of Mathematics, 59030 Merkez-Tekirdağ, Turkey.
چکیده
The simplified phenomenological model of long-crested shallow-water wave propagations is considered without/with the Coriolis effect. Symmetry analysis is taken into consideration to obtain exact solutions. Both classical wave transformation and transformations are obtained with symmetries and solvable equations are kept thanks to these transformations. Additionally, the exact solutions are obtained via various methods which are ansatz-based methods. The obtained results have a major role in the literature so that the considered equation is seen in a large scale of applications in the area of geophysical.
کلیدواژه‌ها
Rotational Green-Naghdi equations؛ Group transformations؛ Exact solutions
مراجع
  • [1]          Y. Y. Bagderina and A. P. Chupakhin, Invariant and Partially Invariant Solutions of The GreenNaghdi Equations, Journal of Applied Mechanics and Technical Physics, 46(6) (2005), 791799.
  • [2]          R. M. Chen, G. Gui, and Y. Liu, On a shallow-water approximation to the GreenNaghdi equa- tions with the Coriolis effect, Advances in Mathematics, 340 (2018), 106137.
  • [3]          A. Constantin, On the modelling of equatorial waves, Geophys. Res. Lett., 39 (2012), L05602.
  • [4]          R. C. Ertekin, M. Hayatdavoodi, and J.W. Kim, On some solitary and cnoidal wave diffraction solutions of the GreenNaghdi equations , Applied Ocean Research, 47 (2014), 125137.
  • [5]          W. Gao, G. Yel, H. M. Baskonus, and C. Cattani, Complex solitons in the conformable (2+1)- dimensional Ablowitz-Kaup-Newell-Segur equation, AIMS Mathematics, 5(1) (2020), 507521.
  • [6]          W. Gao, H. F. Ismael,H. Bulut, and H. M. Baskonus, Instability modulation for the (2+1)- dimension paraxial wave equation and its new optical soliton solutions in Kerr media, Physica Scripta, 95 (2019), 035207 . .
  • [7]          A.E. Green and P.M. Naghdi, A derivation of equations for wave propagation in water of variable depth, J. Fluid Mech, 78 (1976), 237246.
  • [8]          A.E. Green and P.M. Naghdi, On the theory of water waves, Proc R Soc Lond Ser AMath Phys Sci, 338 (1974), 4355.
  • [9]          G. Gui, Y. Liu, and T. Luo, Model Equations and Traveling Wave Solutions for Shallow-Water Waves with the Coriolis Effect, Journal of Nonlinear Science, 29 (2019), 9931039.
  • [10]        G. Guirao, H. M. Baskonus A. Kumar, M. S. Rawat, and G. Yel, Complex Patterns to the (3+1)-Dimensional B-type Kadomtsev-Petviashvili-Boussinesq Equation, Symmetry, 12 (2020). DOI:10.3390/sym12010017.
  • [11]        N. H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, Chich- ester: John Wiley and Sons, (1999).
  • [12]        S. Lie, Geometrie der Berhrungstransformationen, Leipzig: B. G. Teubner, (1896), Reprinted by Chelsea Publishing Company, New York, 1977.
  • [13]        S. Lie, Theorie der Transformationsgruppen I, II and III , Leipzig: B. G. Teubner (1888), Reprinted by Chelsea Publishing Company, New York, 1970.
  • [14]        J.P. Olver,Applications of Lie Groups to Differential Equations (2nd ed.). New York: Springer, (1993).
  • [15]        L.A. Ostrovsky, Nonlinear internal waves in a rotating ocean, Okeanologia,18 (1978), 181191.
  • [16]        L.V. Ovsiannikov, Group Analysis of Differential Equations, Moscow: Nauka (1978). English translation, Ames, W. F., Ed., published by Academic Press, New York, 1982.
  • [17]        Z. Pinar and H. Kocak,Exact solutions for the third-order dispersive-Fisher equations, Nonlinear Dyn, 91 (2018), 421426.
  • [18]        Z. Pnar and T. zis,An observation on the periodic solutions to nonlinear physical models by means of the auxiliary equation with a sixth degree nonlinear term , Communications in Non- linear Science and Numerical Simulation, 18(8) (2013), 2177-2187.
  • [19]        Z. Pnar and T. zis, Classical symmetry analysis and exact solutions for generalized Kortewegde Vries models with variable coefficients, International Journal of Non-Linear Mechanics, 105 (2018), 99104.
  • [20]        Z. Pinar,Simulations of Surface Corrugations of Graphene Sheets via the Generalized Graphene Thermophoretic Motion Equation, International Journal  of  Computational  Materials  Science  and Engineering,9(1) (2020), 20050005. DOI:10.1142/S2047684120500050.
  • [21]        Z. Pinar, The Combination of Conservation Laws and Auxiliary Equation Method , Interna- tional Journal of  Applied  and  Computational  Mathematics  ,6(1)  (2020).  DOI:10.1007/s40819-  019- 0764-2.
  • [22]        Z. Pinar, The symmetry analysis of electrostatic micro-electromechanical system (MEMS), Modern Physics Letters B, 34(18) (2020), 2050199. DOI:10.1142/S0217984920501997.
  • [23]        F. Serre, Contribution ltude des coulements permeanents et variables ands les canaux, Houille Blanche, 3 (1953), 374388.
  • [24]        P. Siriwata and S. V. Meleshko, Group properties of the extended GreenNaghdi equations, Ap- plied Mathematics Letters, 81 (2018), 16.
  • [25]        Y. Wang and Y. Yang, Solitary vortex dynamics of two-dimensional harmonically trapped Bose- Einstein condensates with higher-order nonlinear interactions, AIP Advances, 8 (2018), 095317.
  • [26]        Y. Wang, Q. Chen, J. Guo, and W. Wang, Sonic horizon dynamics for quantum systems with cubic-quintic-septic nonlinearity , AIP Advances, 9 (2019) , 075206.
  • [27]        Y. Wang, S. Li, J. Guo, Y. Zhou, Q. Zhou, and W. Wen, Analytical solution and Soliton-like behavior for the (1+1)-dimensional quantum system with generalized cubic-quintic nonlinearity, International Journal of Bifurcation and Chaos, 26 (2016), 1650195.
  • [28]        Y. Wang, Y. Yang, S. He, and W. Wang, Dynamic evolution of vortex solitons for coupled Bose-Einstein condensates in harmonic potential trap , AIP Advances,7 (2017), 105209.
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