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Traveling wave solutions and conservation laws of a generalized Kudryashov-Sinelshchikov equation

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Kudryashov and Sinelshchikov proposed a nonlinear evolution equation that models the pressure waves in a mixture of liquid and gas bubbles by taking into account the viscosity of the liquid and the heat transfer. Conservation laws and exact solutions are computed for this underlying equation. In the analysis of this particular equation, two approaches are employed, namely, the multiplier method and Kudryashov method.
Wydawca
Rocznik
Strony
211--217
Opis fizyczny
Bibliogr. 18 poz., wykr.
Twórcy
  • Department of Mathematics, Faculty of Science, University of Botswana, Private Bag 22, Gaborone, Botswana
  • Department of Mathematical Sciences, University of South Africa, UNISA 0003, South Africa
  • Department of Mathematical Sciences, Material Science Innovation and Modeling Focus Area, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
Bibliografia
  • [1] B. Bira and T. R. Sekhar, Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis, Appl. Math. Mech. (English Ed.) 36 (2015), no. 8, 1105-1112.
  • [2] J. C. Camacho, M. Rosa, M. L. Gandarias and M. S. Bruzón, Classical symmetries, travelling wave solutions and conservation laws of a generalized Fornberg-Whitham equation, J. Comput. Appl. Math. 318 (2017), 149-155.
  • [3] R. de la Rosa, M. L. Gandarias and M. S. Bruzón, Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation, Commun. Nonlinear Sci. Numer. Simul. 40 (2016), 71-79.
  • [4] Z. T. Fu, S. D. Liu, S. K. Liu and Q. Zhao, New exact solutions to KdV equations with variable coefficients or forcing, Appl. Math. Mech. 25 (2004), no. 1, 67-73.
  • [5] M. L. Gandarias and M. S. Bruzón, Some conservation laws for a forced KdV equation, Nonlinear Anal. Real World Appl. 13 (2012), no. 6, 2692-2700.
  • [6] M. L. Gandarias and M. S. Bruzón, Conservation laws for a Boussinesq equation, Appl. Math. Nonlinear Sci. 2 (2017), no. 2, 465-472.
  • [7] D. J. Korteweg and G. de Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag. (5) 39 (1895), no. 240, 422-443.
  • [8] N. A. Kudryashov, Exact soliton solutions of a generalized evolution equation of wave dynamics, Prikl. Mat. Mekh. 52 (1988), no. 3, 465-470.
  • [9] N. A. Kudryashov, On types of nonlinear nonintegrable equations with exact solutions, Phys. Lett. A 155 (1991), no. 4-5, 269-275.
  • [10] N. A. Kudryashov, One method for finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), no. 6, 2248-2253.
  • [11] N. A. Kudryashov and D. I. Sinelshchikov, Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer, Phys. Lett. A 374 (2010), no. 19, 2011-2016.
  • [12] P. N. Ryabov, Exact solutions of the Kudryashov-Sinelshchikov equation, Appl. Math. Comput. 217 (2010), no. 7, 3585-3590.
  • [13] R. Tracinà, M. S. Bruzón and M. L. Gandarias, On the nonlinear self-adjointness of a class of fourth-order evolution equations, Appl. Math. Comput. 275 (2016), 299-304.
  • [14] J.-M. Tu, S.-F. Tian, M.-J. Xu and T.-T. Zhang, On Lie symmetries, optimal systems and explicit solutions to the Kudryashov-Sinelshchikov equation, Appl. Math. Comput. 275 (2016), 345-352.
  • [15] A.-M. Wazwaz, New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations, Appl. Math. Comput. 182 (2006), no. 2, 1642-1650.
  • [16] A.-M. Wazwaz, The extended tanh method for new solitons solutions for many forms ofh e fifth-order KdV equations, Appl. Math. Comput. 184 (2007), no. 2, 1002-1014.
  • [17] A.-M. Wazwaz, The extended tanh method for the Zakharov-Kuznetsov (ZK) equation, the modified ZK equation, and its generalized forms, Commun. Nonlinear Sci. Numer. Simul. 13 (2008), no. 6, 1039-1047.
  • [18] A. M. Wazwaz, Multi-front waves for extended form of modified Kadomtsev-Petviashvili equation, Appl. Math. Mech. (English Ed.) 32 (2011), no. 7, 875-880.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8dbd0f05-ff1c-4461-909c-325ead36d0f0
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