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Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation


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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. Phil. Mag., 39:422–443, 1895. 10.1080/1478644950862073910.1080/14786449508620739KortewegD. J.de VriesG.On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wavesPhil. Mag.39422443189510.1080/14786449508620739Open DOISearch in Google Scholar

W. X. Ma and B. Fuchssteiner. The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy. Phys. Lett. A, 213:49–55, 1996. 10.1016/0375-9601(96)00112-010.1016/0375-9601(96)00112-0MaW. X.FuchssteinerB.The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchyPhys. Lett. A2134955199610.1016/0375-9601(96)00112-0Open DOISearch in Google Scholar

A. M. Wazwaz. Integrability of coupled KdV equations. Cent. Eur. J. Phy., 9:835–840, 2011. 10.2478/s11534-010-0084-yWazwazM. A.Integrability of coupled KdV equationsCent. Eur. J. Phy.9835840201110.2478/s11534-010-0084-y10.2478/s11534-010-0084-ySearch in Google Scholar

A. M. Wazwaz. Partial Differential Equations and Solitary Waves Theory. Springer, New York, 2009. 10.1007/978-3-642-00251-9WazwazM. A.Partial Differential Equations and Solitary Waves Theory.SpringerNew York200910.1007/978-3-642-00251-910.1007/978-3-642-00251-9Search in Google Scholar

A. R. Adem and C. M. Khalique. On the solutions and conservation laws of a coupled KdV system. Appl. Math. Comput., 219:959–969, 2012. 10.1016/j.amc.2012.06.076AdemA. R.KhaliqueM. C.On the solutions and conservation laws of a coupled KdV systemAppl. Math. Comput.219959969201210.1016/j.amc.2012.06.07610.1016/j.amc.2012.06.076Search in Google Scholar

D. S. Wang. Integrability of a coupled KdV system: Painlevé property, Lax pair and Bäcklund transformation. Appl. Math. Comput., 216:1349–1354, 2010. 10.1016/j.amc.2010.02.030WangS. D.Integrability of a coupled KdV system: Painlevé property, Lax pair and Bäcklund transformationAppl. Math. Comput.21613491354201010.1016/j.amc.2010.02.03010.1016/j.amc.2010.02.030Search in Google Scholar

C. X. Li. A Hierarchy of Coupled Korteweg-de Vries Equations and the Corresponding Finite-Dimensional Integrable System. J. Phys. Soc. Jpn., 73:327–331, 2004. 10.1143/JPSJ.73.32710.1143/JPSJ.73.327LiX. C.A Hierarchy of Coupled Korteweg-de Vries Equations and the Corresponding Finite-Dimensional Integrable SystemJ. Phys. Soc. Jpn.73327331200410.1143/JPSJ.73.327Open DOISearch in Google Scholar

Z. Qin. A finite-dimensional integrable system related to a new coupled KdV hierarchy. Phys. Lett. A, 355:452–459, 2006. 10.1016/j.physleta.2005.09.08910.1016/j.physleta.2005.09.089QinZ.A finite-dimensional integrable system related to a new coupled KdV hierarchyPhys. Lett. A355452459200610.1016/j.physleta.2005.09.089Open DOISearch in Google Scholar

A. M. Wazwaz. Solitons and periodic wave solutions for coupled nonlinear equations. Int. J. Nonlinear Sci., 14:266–277, 2012.WazwazM. A.Solitons and periodic wave solutions for coupled nonlinear equationsInt. J. Nonlinear Sci.142662772012Search in Google Scholar

W. X. Ma and B. Fuchssteiner. Integrable theory of the perturbation equations. Chaos Solitons Fractals, 7(8):1227–1250, 1996. 10.1016/0960-0779(95)00104-210.1016/0960-0779(95)00104-2MaW. X.FuchssteinerB.Integrable theory of the perturbation equationsChaos Solitons Fractals7812271250199610.1016/0960-0779(95)00104-2Open DOISearch in Google Scholar

W. X. Ma. A bi-Hamiltonian formulation for triangular systems by perturbations. J. Math. Phys., 43:1408–1421, 2002. 10.1063/1.143277510.1063/1.1432775MaX. W.A bi-Hamiltonian formulation for triangular systems by perturbationsJ. Math. Phys.4314081421200210.1063/1.1432775Open DOISearch in Google Scholar

M. Wang, Y. Zhou, and Z. Li. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys. Lett. A, 216:67–75, 1996. 10.1016/0375-9601(96)00283-610.1016/0375-9601(96)00283-6WangM.ZhouY.LiZ.Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physicsPhys. Lett. A2166775199610.1016/0375-9601(96)00283-6Open DOISearch in Google Scholar

J. Hu and H. Zhang. A new method for finding exact traveling wave solutions to nonlinear partial differential equations. Phys. Lett. A, 286:175–179, 2001.10.1016/S0375-9601(01)00291-2HuJ.ZhangH.A new method for finding exact traveling wave solutions to nonlinear partial differential equationsPhys. Lett. A2861751792001Open DOISearch in Google Scholar

M. J. Ablowitz and P. A. Clarkson. Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge, 1991. 10.1017/CBO9780511623998AblowitzM. J.ClarksoP. A.Solitons, Nonlinear Evolution Equations and Inverse Scattering.Cambridge University PressCambridge199110.1017/CBO978051162399810.1017/CBO9780511623998Search in Google Scholar

C. H. Gu. Soliton Theory and its Application. Zhejiang Science and Technology Press, Zhejiang, 1990.GuH. C.Soliton Theory and its Application.Zhejiang Science and Technology PressZhejiang1990Search in Google Scholar

V. B. Matveev and M. A. Salle. Darboux Transformations and Solitons. Springer-Verlag, Berlin, 1991. 10.1007/978-3-662-00922-2MatveevV. B.SalleA. M.Darboux Transformations and Solitons.Springer-VerlagBerlin199110.1007/978-3-662-00922-210.1007/978-3-662-00922-2Search in Google Scholar

R. Hirota. The Direct Method in Soliton Theory. Cambridge University Press, Cambridge, 2004.HirotaR.The Direct Method in Soliton Theory.Cambridge University PressCambridge200410.1017/CBO9780511543043Search in Google Scholar

N. A. Kudryashov. Exact solitary waves of the Fisher equation. Phys. Lett. A, 342:99-106, 2005. 10.1016/j.physleta.2005.05.02510.1016/j.physleta.2005.05.025KudryashovA. N.Exact solitary waves of the Fisher equationPhys. Lett. A34299106200510.1016/j.physleta.2005.05.025Open DOISearch in Google Scholar

M. Wang, X. Li, and J. Zhang. The (G’/G)–expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A, 372:417-423, 2008. 10.1016/j.physleta.2007.07.05110.1016/j.physleta.2007.07.051WangM.LiX.ZhangJ.The (G’/G)–expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physicsPhys. Lett. A372417423200810.1016/j.physleta.2007.07.051Open DOISearch in Google Scholar

T. Aziz, T. Motsepa, A. Aziz, A. Fatima, and C. M. Khalique. Classical model of Prandtl’s boundary layer theory for radial viscous flow: application of (G’/G)–expansion method. J. Comput. Anal. Appl., 23:31–41, 2017.AzizT.MotsepaT.AzizA.FatimaA.KhaliqueM. C.Classical model of Prandtl’s boundary layer theory for radial viscous flow: application of (G’/G)–expansion methodJ. Comput. Anal. Appl.2331412017Search in Google Scholar

Z. Zhang. Jacobi elliptic function expansion method for the modified Korteweg-de Vries-Zakharov-Kuznetsov and the Hirota equations. Phys. Lett. A, 289:69–74, 2001.ZhangZ.Jacobi elliptic function expansion method for the modified Korteweg-de Vries-Zakharov-Kuznetsov and the Hirota equationsPhys. Lett. A2896974200110.1016/S0375-9601(01)00580-1Search in Google Scholar

N. A. Kudryashov. One method for finding exact solutions of nonlinear differential equations. Commun Nonlinear Sci. Numer. Simulat., 17:2248–2253, 2012. 10.1016/j.cnsns.2011.10.01610.1016/j.cnsns.2011.10.016KudryashovA. N.One method for finding exact solutions of nonlinear differential equationsCommun Nonlinear Sci. Numer. Simulat.1722482253201210.1016/j.cnsns.2011.10.016Open DOISearch in Google Scholar

P. J. Olver. Applications of Lie Groups to Differential Equations. Springer-Verlag, Berlin, 1993. 10.1007/978-1-4612-4350-2OlverJ. P.Applications of Lie Groups to Differential Equations.Springer-VerlagBerlin199310.1007/978-1-4612-4350-210.1007/978-1-4612-4350-2Search in Google Scholar

G. W. Bluman and S. Kumei. Symmetries and Differential Equations. Springer-Verlag, New York, 1989. 10.1007/978-1-4757-4307-4BlumanG. W.KumeiS.Symmetries and Differential Equations.Springer-VerlagNew York198910.1007/978-1-4757-4307-410.1007/978-1-4757-4307-4Search in Google Scholar

N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations. Vols. 1–3, CRC Press, Boca Raton, FL, 1994–1996.IbragimovN. H.CRC Handbook of Lie Group Analysis of Differential Equations13CRC PressBoca Raton, FL19941996Search in Google Scholar

T. Motsepa, C. M. Khalique, and M. L. Gandarias. Symmetry analysis and conservation laws of the Zoomeron equation. Symmetry, 9, 2017, 11 pages.MotsepaT.KhaliqueC. M.GandariasL. M.Symmetry analysis and conservation laws of the Zoomeron equationSymmetry920171110.3390/sym9020027Search in Google Scholar

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., 318:149–155, 2017. 10.1016/j.cam.2016.11.01710.1016/j.cam.2016.11.017CamachoJ. C.RosaM.GandariasM. L.BruzónM. S.Classical symmetries, travelling wave solutions and conservation laws of a generalized Fornberg-Whitham equationJ. Comput. Appl. Math.318149155201710.1016/j.cam.2016.11.017Open DOISearch in Google Scholar

M. Rosa, J. C. Camacho, M. S. Bruzón, and M.L. Gandarias. Classical and potential symmetries for a generalized Fisher equation. J. Comput. Appl. Math., 318:181–188, 2017. 10.1016/j.cam.2016.10.02810.1016/j.cam.2016.10.028RosaM.CamachoJ. C.BruzónM. S.GandariasM.L.Classical and potential symmetries for a generalized Fisher equationJ. Comput. Appl. Math.318181188201710.1016/j.cam.2016.10.028Open DOISearch in Google Scholar

H. Steudel. Uber die Zuordnung zwischen invarianzeigenschaften und Erhaltungssatzen. Z Naturforsch, 17A:129–132, 1962.SteudelH.Uber die Zuordnung zwischen invarianzeigenschaften und ErhaltungssatzenZ Naturforsch17129132196210.1515/zna-1962-0204Search in Google Scholar

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. Appl. Math.13545566200210.1017/S095679250100465XSearch in Google Scholar

T. Motsepa and C. M. Khalique. Conservation laws and solutions of a generalized coupled (2+1)-dimensional Burgers system. Comput. Math. Appl., 74:1333–1339, 2017. 10.1016/j.camwa.2017.06.01510.1016/j.camwa.2017.06.015MotsepaT.KhaliqueM. C.Conservation laws and solutions of a generalized coupled (2+1)-dimensional Burgers systemComput. Math. Appl.7413331339201710.1016/j.camwa.2017.06.015Open DOISearch in Google Scholar

A. Fatima, F. M. Mahomed, and C. M. Khalique. Noether symmetries and exact solutions of an Euler-Bernoulli beam model. Int. J. of Mod Phys B, 30:1640011, 2016. 10.1142/S021797921640011710.1142/S0217979216400117FatimaA.MahomedF. M.KhaliqueM. C.Noether symmetries and exact solutions of an Euler-Bernoulli beam modelInt. J. of Mod Phys B301640011201610.1142/S0217979216400117Open DOISearch in Google Scholar

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. 10.1016/j.rinp.2017.10.04110.1016/j.rinp.2017.10.041SimbanefayiI.KhaliqueM. C.Travelling wave solutions and conservation laws for the Korteweg-de Vries- Bejamin-Bona-Mahony equationResults in Physics85763201810.1016/j.rinp.2017.10.041Open DOISearch in Google Scholar

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. 10.21042/AMNS.2016.1.0002110.21042/AMNS.2016.1.00021de laRosaR.BruzónM. S.On the classical and nonclassical symmetries of a generalized Gardner equationApplied Mathematics and Nonlinear Sciences11263272201610.21042/AMNS.2016.1.00021Open DOISearch in Google Scholar

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. 10.21042/AMNS.2016.2.0002610.21042/AMNS.2016.2.00026RosaM.GandariasL. M.Multiplier method and exact solutions for a density dependent reaction-diffusion equationApplied Mathematics and Nonlinear Sciences12311320201610.21042/AMNS.2016.2.00026Open DOISearch in Google Scholar

M. L. Gandarias and M. S. Bruzón. Conservation laws for a Boussinesq equation. Applied Mathematics and Nonlinear Sciences, 2(2):465–472, 2017. 10.21042/AMNS.2017.2.0003710.21042/AMNS.2017.2.00037GandariasM. L.BruzónM. S.Conservation laws for a Boussinesq equationApplied Mathematics and Nonlinear Sciences22465472201710.21042/AMNS.2017.2.00037Open DOISearch in Google Scholar

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. 10.1515/phys-2018-003010.1515/phys-2018-0030MotsepaT.KhaliqueC. M.On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physicsOpen Phys.16211214201810.1515/phys-2018-0030Open DOISearch in Google Scholar

A. F. Cheviakov. GeM software package for computation of symmetries and conservation laws of differential equations. Comput. Phys. Commun., 176:48–61, 2007. 10.1016/j.cpc.2006.08.00110.1016/j.cpc.2006.08.001CheviakovF. A.GeM software package for computation of symmetries and conservation laws of differential equationsComput. Phys. Commun.1764861200710.1016/j.cpc.2006.08.001Open DOISearch in Google Scholar

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