On optimal system, exact solutions and conservation laws of the modified equal-width equation

[1]D. Lu, A. R. Seadawy, A. Ali. Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications. Results in Physics 9 (2018): 313-320.LuD.SeadawyA. R.AliA.Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applicationsResults in Physics92018313–32010.1016/j.rinp.2018.02.036Search in Google Scholar

[2]H. Wang, L. Chen, H. Wang, Exact travelling wave solutions of the modified equal width equation via the dynamical system method, Nonlinear Analysis and Differential Equations, 4 (2016) 9–15.WangH.ChenL.WangH.Exact travelling wave solutions of the modified equal width equation via the dynamical system methodNonlinear Analysis and Differential Equations420169–1510.12988/nade.2016.5824Search in Google Scholar

[3]S.T. Mohyud-Din, A. Yildirim, M.E. Berberler, M. M. Hosseini, Numerical Solution of Modified Equal Width Wave Equation, World Applied Sciences Journal 8 (2010) 792–798Mohyud-DinS.T.YildirimA.BerberlerM.E.HosseiniM. M.Numerical Solution of Modified Equal Width Wave EquationWorld Applied Sciences Journal82010792–798Search in Google Scholar

[4]L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982.OvsiannikovL.V.Group Analysis of Differential EquationsAcademic PressNew York198210.1016/B978-0-12-531680-4.50012-5Search in Google Scholar

[5]G.W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York, 1989.BlumanG.W.KumeiS.Symmetries and Differential EquationsSpringer-VerlagNew York198910.1007/978-1-4757-4307-4Search in Google Scholar

[6]P.J. Olver, Applications of Lie Groups to Differential Equations, second ed., Springer-Verlag, Berlin, 1993.OlverP.J.Applications of Lie Groups to Differential Equations, second edSpringer-VerlagBerlin199310.1007/978-1-4612-4350-2Search in Google Scholar

[7]N.H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Vols 1–3, CRC Press, Boca Raton, Florida, 1994–1996.IbragimovN.H.CRC Handbook of Lie Group Analysis of Differential EquationsVols1–3CRC PressBoca Raton, Florida1994–1996Search in Google Scholar

[8]N.H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley & Sons, Chichester, NY, 1999.IbragimovN.H.Elementary Lie Group Analysis and Ordinary Differential EquationsJohn Wiley & SonsChichester, NY1999Search in Google Scholar

[9]T. Motsepa, C.M. Khalique, Cnoidal and snoidal waves solutions and conservation laws of a generalized (2+1)-dimensional KdV equation, Proceedings of the 14th Regional Conference on Mathematical Physics, 2018, Pages: 253–263 10.1142/9789813224971-0027MotsepaT.KhaliqueC.M.Cnoidal and snoidal waves solutions and conservation laws of a generalized (2+1)-dimensional KdV equationProceedings of the 14th Regional Conference on Mathematical Physics2018Pages253–26310.1142/9789813224971-002710.1142/9789813224971_0027Search in Google Scholar

[10]I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, 7th edn. Academic Press, New York, 2007.GradshteynI.S.RyzhikI.M.Table of Integrals, Series, and Products, 7th ednAcademic PressNew York2007Search in Google Scholar

[11]S. Anco and G. Bluman. Direct construction method for conservation laws of partial differential equations Part I: Examples of conservation law classifications. European J. Appl. Math., 13:545–566, 2002.AncoS.BlumanG.Direct construction method for conservation laws of partial differential equations Part I: Examples of conservation law classificationsEuropean J. ApplMath13545–566200210.1017/S095679250100465XSearch in Google Scholar

[12]I. Simbanefayi and C.M. Khalique. Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation. Results in Physics, 8:57–63, 2018.SimbanefayiI.KhaliqueC.M.Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equationResults in Physics857–63201810.1016/j.rinp.2017.10.041Search in Google Scholar

[13]M. Rosa and M.L. Gandarias. Multiplier method and exact solutions for a density dependent reaction-diffusion equation. Applied Mathematics and Nonlinear Sciences, 1(2):311–320, 2016.RosaM.GandariasM.L.Multiplier method and exact solutions for a density dependent reaction-diffusion equationApplied Mathematics and Nonlinear Sciences12311–320201610.21042/AMNS.2016.2.00026Search in Google Scholar

[14]R. de la Rosa and M.S. Bruzón. On the classical and nonclassical symmetries of a generalized Gardner equation. Applied Mathematics and Nonlinear Sciences, 1(1):263–272, 2016.de la RosaR.BruzónM.S.On the classical and nonclassical symmetries of a generalized Gardner equationApplied Mathematics and Nonlinear Sciences11263–272201610.21042/AMNS.2016.1.00021Search in Google Scholar

[15]M.L. Gandarias and M.S. Bruzón. Conservation laws for a Boussinesq equation. Applied Mathematics and Nonlinear Sciences, 2(2):465–472, 2017.GandariasM.L.BruzónM.S.Conservation laws for a Boussinesq equationApplied Mathematics and Nonlinear Sciences22465–472201710.21042/AMNS.2017.2.00037Search in Google Scholar

[16]T. Motsepa and C.M. Khalique. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics. Open Phys., 16:211–214, 2018.MotsepaT.KhaliqueC.M.On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physicsOpen Phys16211–214201810.1515/phys-2018-0030Search in Google Scholar

[17]C.M. Khalique, I.E. Mhlanga. Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation. Applied Mathematics and Nonlinear Sciences, 2018, in press.KhaliqueC.M.MhlangaI.E.Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation. Applied Mathematics and Nonlinear Sciences, 2018in press10.21042/AMNS.2018.1.00018Search in Google Scholar

[18]E. Noether, Invariante variationsprobleme, Nachr. König. Gesell. Wissen., Göttingen. Math Phys Kl Heft, 2 (1918) 235–257. English translation in Transp. Theor. Stat. Phys. 1(3) (1971) 186–207.NoetherE.Invariante variationsprobleme, Nachr. König. Gesell. Wissen., GöttingenMath Phys Kl Heft21918235–257English translation in Transp. Theor. Stat. Phys. 1(3) (1971) 186–207Search in Google Scholar

[19]T. Motsepa, M. Abudiab, C.M. Khalique, A study of an extended generalized (2+1)-dimensional Jaulent-Miodek equation, Int. J. Nonlinear Sci. Numer. Simul. 19 (3–4) (2018) In Press.MotsepaT.AbudiabM.KhaliqueC.M.A study of an extended generalized (2+1)-dimensional Jaulent-Miodek equationInt. J. Nonlinear Sci. Numer. Simul193–42018In Press10.1515/ijnsns-2017-0147Search in Google Scholar

[20]W. Sarlet. Comment on ‘conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives’. Journal of Physics A: Mathematical and Theoretical 43.45 (2010): 458001.SarletW.Comment on ‘conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives’Journal of Physics A: Mathematical and Theoretical43.45201045800110.1088/1751-8113/43/45/458001Search in Google Scholar