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2015 | 128 | 3 | 252-255
Article title

Lie Symmetry Reductions, Exact Solutions and Conservation Laws of the Third Order Variant Boussinesq System

Content
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EN
Abstracts
EN
The Lie group method is applied to the third order variant Boussinesq system, which arises in the modelling of the water waves. The symmetry reductions and invariant solutions are obtained with respect to Lie point symmetry generators of the underlying system. In addition, we derive conservation laws of the variant Boussinesq system.
Keywords
EN
Year
Volume
128
Issue
3
Pages
252-255
Physical description
Dates
published
2015-09
received
2015-03-27
References
  • [1] V.O. Vakhnenko, E.J. Parkes, A.J. Morrison, Chaos Solitons Fract. 17, 683 (2003), doi: 10.1016/S0960-0779(02)00483-6
  • [2] R. Hirota, Phys. Rev. Lett. 27, 1192 (1971), doi: 10.1103/PhysRevLett.27.1192
  • [3] Y. Ma, X. Geng, Appl. Math. Comput. 218, 6963 (2012), doi: 10.1016/j.amc.2011.12.077
  • [4] A. Zerarka, S. Ouamane, S. Attaf, Appl. Math. Comput. 217, 2897 (2010), doi: 10.1016/j.amc.2010.08.070
  • [5] M.L. Wang, Y.B. Zhou, Z.B. Li, Phys. Lett. A 216, 67 (1996), doi: 10.1016/0375-9601(96)00283-6
  • [6] A. Bekir, Commun. Nonlin. Sci. Numer. Simulat. 13, 1748 (2008), doi: 10.1016/j.cnsns.2007.05.001
  • [7] A. Bekir, Phys. Lett. A 372, 3400 (2008), doi: 10.1016/j.physleta.2008.01.057
  • [8] E. Fan, Y.C. Hon, Chaos Solitons Fract. 15, 559 (2003), doi: 10.1016/S0960-0779(02)00144-3
  • [9] B. Muatjetjeja, C.M. Khalique, Abstract Appl. Anal. 2014, 169694 (2014), doi: 10.1155/2014/169694
  • [10] M. Wang, Phys. Lett. A 199, 169 (1995), doi: 10.1016/0375-9601(95)00092-H
  • [11] R. Naz, F.M. Mahomed, T. Hayat, Appl. Math. Lett. 23, 883 (2010), doi: 10.1016/j.aml.2010.04.003
  • [12] I.M. Anderson, M.E. Fels, C.G. Torre, Commun. Math. Phys. 212, 653 (2000), doi: 10.1007/s002200000215
  • [13] G.W. Bluman, S.C. Anco, Symmetry and Integration Methods for Differential Equations, Vol. 154 of Applied Mathematical Sciences, Springer, New York 2002
  • [14] P.J. Olver, Application of Lie Groups to Differential Equations, Springer-Verlag, New York 1993
  • [15] N.H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 1, Symmetries, Exact Solutions and Conservation Laws, CRC Press, Boca Raton, Florida 1995
  • [16] C. Rogers, W. Shadwick, Nonlinear Boundary Value Problems in Science and Engineering, Mathematics in Science and Enginering, Vol. 183, Ed. W.F. Ames, Academic Press, Boston 1989
  • [17] N.H. Ibragimov, R. Khamitova, B. Thide, J. Math. Phys. 48, 053523 (2007), doi: 10.1063/1.2735822
  • [18] A.F. Cheviakov, Comput. Phys. Commun. 176, 48 (2007), doi: 10.1016/j.cpc.2006.08.001
  • [19] H. Steudel, Z. Naturforsch. 17A, 129 (1962), doi: 10.1515/zna-1962-0204
  • [20] A.H. Kara, F.M. Mahomed, Int. J. Theor. Phys. 39, 23 (2000), doi: 10.1023/A:1003686831523
  • [21] A.H. Kara, F.M. Mahomed, Nonlinear Dynam. 45, 367 (2006), doi: 10.1007/s11071-005-9013-9
  • [22] S.C. Anco, G.W. Bluman, Eur. J. Appl. Math. 13, 545 (2002), doi: 10.1017/S095679250100465X
  • [23] A.R. Adem, C.M. Khalique, Comput. Fluids 81, 10 (2013), doi: 10.1016/j.compfluid.2013.04.005
  • [24] A.R. Adem, C.M. Khalique, Commun. Nonlin. Sci. Numer. Simulat. 17, 3465 (2012), doi: 10.1016/j.cnsns.2012.01.010
  • [25] H. Triki, A.H. Kara, A.H. Bhrawy, A. Biswas, Acta Phys. Pol. A 125, 1099 (2014), doi: 10.12693/APhysPolA.125.1099
  • [26] I.E. Mhlanga, C.M. Khalique, J. Appl. Math. 2012, 389017 (2012), doi: 10.1155/2012/389017
  • [27] N.H. Ibragimov, J. Math. Anal. Appl. 333, 311 (2007), doi: 10.1016/j.jmaa.2006.10.078
  • [28] N.A. Kudryashov, Chaos Solitons Fract. 24, 1217 (2005), doi: 10.1016/j.chaos.2004.09.109
  • [29] N.A. Kudryashov, Phys. Lett. A 342, 99 (2005), doi: 10.1016/j.physleta.2005.05.025
  • [30] H. Jafari, N. Kadkhoda, C.M. Kahlique, Abstract Appl. Anal. 2012, 350287 (2012), doi: 10.1155/2012/350287
  • [31] R.J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics, Birkhauser Verlag, Basel 1992
  • [32] T. Wolf, Europ. J. Appl. Math. 2, 129 (2002), doi: 10.1017/S0956792501004715
  • [33] A.H. Bokhari, A.Y. Al-Dweik, A.H. Kara, F.M. Mahomed, F.D. Zaman, Commun. Nonlin. Sci. Numer. Simulat. 16, 1244 (2011), doi: 10.1016/j.cnsns.2010.07.007
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv128n302kz
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