Symmetry Reductions for a Generalized Fifth Order KdV Equation

[1]Abramowitz, M. and Stegun, I.A. (1965), Handbook of mathematical functions, Applied Mathematics series - 55, United States.AbramowitzM.StegunI.A.1965Handbook of mathematical functionsApplied Mathematics series - 55United States10.1119/1.1972842Search in Google Scholar

[2]Anco S.C., Bluman G. (1997), Direct construction of conservation laws from field equations, Phys. Rev. Lett. 78: 2869. 10.1103/physrevlett.78.2869AncoS.C.BlumanG.1997Direct construction of conservation laws from field equationsPhys. Rev. Lett78286910.1103/physrevlett.78.2869Open DOISearch in Google Scholar

[3]Anco, S.C. and Bluman, G. (2002), Direct construction method for conservation laws of partial differential equations, Part I: Examples of conservation law classifications, European Journal of Applied Mathematics 13(5): 545-566. 10.1017/S095679250100465XAncoS.C.BlumanG.2002Direct construction method for conservation laws of partial differential equations, Part I: Examples of conservation law classificationsEuropean Journal of Applied Mathematics13554556610.1017/S095679250100465XOpen DOISearch in Google Scholar

[4]Anco, S.C. and Bluman, G. (2002), Direct construction method for conservation laws of partial differential equations, Part II: General treatment, European Journal of Applied Mathematics 13(5): 567-585. 10.1017/S0956792501004661AncoS.C.BlumanG.2002Direct construction method for conservation laws of partial differential equations, Part II: General treatmentEuropean Journal of Applied Mathematics13556758510.1017/S0956792501004661Open DOISearch in Google Scholar

[5]Anco, S.C. (2015), Symmetry Properties of Conservation Laws, Int. J. Mod. Phys. B 30: 1640003. 10.1142/S0217979216400038AncoS.C.2015Symmetry Properties of Conservation LawsInt. J. Mod. PhysB30164000310.1142/S0217979216400038Open DOISearch in Google Scholar

[6]Bokhari, A.H., Al-Dweik, A.Y., Kara, A.H., Mahomed, F.M. and Zaman, F.D. (2011), Double reduction of a nonlinear (2 + 1) wave equation via conservation laws, Communications in Nonlinear Science and Numerical Simulation 16(3): 1244-1253. 10.1016/j.cnsns.2010.07.007BokhariA.H.Al-DweikA.Y.KaraA.H.MahomedF.M.ZamanF.D.2011Double reduction of a nonlinear (2 + 1) wave equation via conservation lawsCommunications in Nonlinear Science and Numerical Simulation1631244125310.1016/j.cnsns.2010.07.007Open DOISearch in Google Scholar

[7]Bakodah, H.O. (2013), Modified Adomain Decomposition Method for the Generalized Fifth Order KdV Equations, American Journal of Computational Mathematics 3(1): 53-58. 10.4236/ajcm.2013.31008BakodahH.O.2013Modified Adomain Decomposition Method for the Generalized Fifth Order KdV EquationsAmerican Journal of Computational Mathematics31535810.4236/ajcm.2013.31008Open DOISearch in Google Scholar

[8]Brown, D.L., Cortez, R. and Minion, M.L. (2001), Accurate Projection Methods for the Incompressible Navier–Stokes Equations, Journal of Computational Physics 168(2): 464-499. 10.1006/jcph.2001.6715BrownD.L.CortezR.MinionM.L.2001Accurate Projection Methods for the Incompressible Navier–Stokes EquationsJournal of Computational Physics168246449910.1006/jcph.2001.6715Open DOISearch in Google Scholar

[9]Bruzón M.S., Garrido, T.M. and de la Rosa, R. (2016), Conservation laws and exact solutions of a Generalized Benjamin–Bona–Mahony–Burgers equation, Chaos, Solitons & Fractals 89: 578-583. 10.1016/j.chaos.2016.03.034BruzónM.S.GarridoT.M.de la RosaR.2016Conservation laws and exact solutions of a Generalized Benjamin–Bona–Mahony–Burgers equation, ChaosSolitons & Fractals8957858310.1016/j.chaos.2016.03.034Open DOISearch in Google Scholar

[10]Bruzón, M.S. and Márquez, A.P. (2017), Conservation laws of one–dimensional strain–limiting viscoelasticity model, AIP Conference Proceedings 1836(1): 020081. 10.1063/1.4982021BruzónM.S.MárquezA.P.2017Conservation laws of one–dimensional strain–limiting viscoelasticity modelAIP Conference Proceedings1836102008110.1063/1.4982021Open DOISearch in Google Scholar

[11]Bruzón, M. S., Recio, E., Garrido, T. M. and Márquez, A. P. (2017), Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation, Open Physics 15(1): 433-439. 10.1515/phys-2017-0048BruzónM. S.RecioE.GarridoT. M.MárquezA. P.2017Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equationOpen Physics15143343910.1515/phys-2017-0048Open DOISearch in Google Scholar

[12]Caraffini, G.L. and Galvani, M. (2012), Symmetries and exact solutions via conservation laws for some partial differential equations of Mathematical Physics, Applied Mathematics and Computation 219(4): 1474-1484. 10.1016/j.amc.2012.07.050CaraffiniG.L.GalvaniM.2012Symmetries and exact solutions via conservation laws for some partial differential equations of Mathematical PhysicsApplied Mathematics and Computation21941474148410.1016/j.amc.2012.07.050Open DOISearch in Google Scholar

[13]de la Rosa, R. and Bruzón, M.S. (2016), On the classical and nonclassical symmetries of a generalized Gardner equation, Applied Mathematics and Nonlinear Sciences 1(1): 263-272. 10.21042/AMNS.2016.1.00021de la RosaR.BruzónM.S.2016On the classical and nonclassical symmetries of a generalized Gardner equationApplied Mathematics and Nonlinear Sciences1126327210.21042/AMNS.2016.1.00021Open DOISearch in Google Scholar

[14]de la Rosa, R., Gandarias, M.L. and Bruzón, M.S. (2016), On symmetries and conservation laws of a Gardner equation involving arbitrary functions, Applied Mathematics and Computation 290: 125-134. 10.1016/j.amc.2016.05.050de la RosaR.GandariasM.L.BruzónM.S.2016On symmetries and conservation laws of a Gardner equation involving arbitrary functionsApplied Mathematics and Computation29012513410.1016/j.amc.2016.05.050Open DOISearch in Google Scholar

[15]de la Rosa, R., Gandarias, M.L. and Bruzón, M.S. (2016), Symmetries and conservation laws of a fifth–order KdV equation with time–dependent coefficients and linear damping, Nonlinear Dynamics 84(1): 135-141. 10.1007/s11071-015-2254-3de la RosaR.GandariasM.L.BruzónM.S.2016Symmetries and conservation laws of a fifth–order KdV equation with time–dependent coefficients and linear dampingNonlinear Dynamics84113514110.1007/s11071-015-2254-3Open DOISearch in Google Scholar

[16]Einstein, A. (1905), The Field Equations of Gravitation, On a Heuristic Point of View about the Creation and Conversion of Light, Annalen der Physik 322(6): 132-148. 10.1002/andp.19053220607EinsteinA.1905The Field Equations of Gravitation, On a Heuristic Point of View about the Creation and Conversion of LightAnnalen der Physik322613214810.1002/andp.19053220607Open DOISearch in Google Scholar

[17]Gandarias, M.L. and Bruzón, M.S. (2012), Some conservation laws for a forced KdV equation, Nonlinear Analysis: Real World Applications 13(6): 2692-2700. doi 10.1016/j.nonrwa.2012.03.013GandariasM.L.BruzónM.S.2012Some conservation laws for a forced KdV equationNonlinear Analysis: Real World Applications1362692270010.1016/j.nonrwa.2012.03.013Open DOISearch in Google Scholar

[18]Gandarias, M.L. and Khalique, C.M. (2016), Symmetries, solutions and conservation laws of a class of nonlinear dispersive wave equations, Communications in Nonlinear Science and Numerical Simulation 32: 114-121. 10.1016/j.cnsns.2015.07.010GandariasM.L.KhaliqueC.M.2016Symmetries, solutions and conservation laws of a class of nonlinear dispersive wave equationsCommunications in Nonlinear Science and Numerical Simulation3211412110.1016/j.cnsns.2015.07.010Open DOISearch in Google Scholar

[19]Garrido, T. M. and Bruzón, M. S. (2016), Lie Point Symmetries and Travelling Wave Solutions for the Generalized Drinfeld–Sokolov System, Journal of Computational and Theoretical Transport 45(4): 290-298. 10.1080/23324309.2016.1164720GarridoT. M.BruzónM. S.2016Lie Point Symmetries and Travelling Wave Solutions for the Generalized Drinfeld–Sokolov SystemJournal of Computational and Theoretical Transport45429029810.1080/23324309.2016.1164720Open DOISearch in Google Scholar

[20]Garrido, T. M., Kasatkin, A. A., Bruzón, M. S. and Gazizov, R. K. (2017), Lie symmetries and equivalence transformations for the Barenblatt–Gilman model, Journal of Computational and Applied Mathematics 318: 253-258. 10.1016/j.cam.2016.09.023GarridoT. M.KasatkinA. A.BruzónM. S.GazizovR. K.2017Lie symmetries and equivalence transformations for the Barenblatt–Gilman modelJournal of Computational and Applied Mathematics31825325810.1016/j.cam.2016.09.023Open DOISearch in Google Scholar

[21]Moleleki, L.D., and Khalique, C.M. (2014), Symmetries, Traveling Wave Solutions, and Conservation Laws of a (3 + 1) Dimensional Boussinesq Equation, Advances in Mathematical Physics 2014: Article ID 672679. 10.1155/2014/672679MolelekiL.D.KhaliqueC.M.2014Symmetries, Traveling Wave Solutions, and Conservation Laws of a (3 + 1) Dimensional Boussinesq EquationAdvances in Mathematical Physics 2014: Article ID 67267910.1155/2014/672679Open DOISearch in Google Scholar

[22]Olver, P.J. (1993), Applications of Lie groups to differential equations. 2nd ed., Graduate Texts in Mathematics, Springer-Verlag, Berlin.OlverP.J.1993Applications of Lie groups to differential equations. 2nd ed.Graduate Texts in MathematicsSpringer-VerlagBerlin10.1007/978-1-4612-4350-2Search in Google Scholar

[23]Sjöberg, A., Double reduction of PDEs from the association of symmetries with conservation laws with applications, Applied Mathematics and Computation 184(2): 608-616. 10.1016/j.amc.2006.06.059SjöbergA.Double reduction of PDEs from the association of symmetries with conservation laws with applicationsApplied Mathematics and Computation184260861610.1016/j.amc.2006.06.059Open DOISearch in Google Scholar

[24]Xu, K. (2001), A Gas-Kinetic BGK Scheme for the Navier–Stokes Equations and Its Connection with Artificial Dissipation and Godunov Method, Journal of Computational Physics 171(1): 289-335. 10.1006/jcph.2001.6790XuK.2001A Gas-Kinetic BGK Scheme for the Navier–Stokes Equations and Its Connection with Artificial Dissipation and Godunov MethodJournal of Computational Physics171128933510.1006/jcph.2001.6790Open DOISearch in Google Scholar

[25]Yu-Qi, L., Jun-Chao, C., Yong C. and Sen-Yue, L. (2014), Darboux Transformations via Lie Point Symmetries: KdV Equation, Chinese Physics Letters 31(1): 010201. 10.1088/0256-307X/31/1/010201Yu-QiL.Jun-ChaoC.YongC.Sen-YueL.2014Darboux Transformations via Lie Point Symmetries: KdV EquationChinese Physics Letters31101020110.1088/0256-307X/31/1/010201Open DOISearch in Google Scholar