667
Views
14
CrossRef citations to date
0
Altmetric
Original Article

Traveling wave solutions of KdVs using sine–cosine methodFootnote

&
Pages 90-93 | Received 05 Jun 2012, Accepted 31 Mar 2013, Published online: 27 Mar 2018

References

  • S.AbbasbandyA new application of He’s variational iteration method for quadratic Riccati differential equation by using Adomian’s polynomialsJ. Comput. Appl. Math.20720075963
  • M.A.AbdouA.A.SolimanNew applications of variational iteration methodPhysics D2111–2200518
  • M.J.AblowitzP.A.ClarksonSolitons, Nonlinear Evolution Equations and Inverse Scattering Transform1991Cambridge Univ. PressCambridge
  • Z.I.A.Al-MuhiameedE.A.B.Abdel-SalamGeneralized Jacobi elliptic function solution to a class of nonlinear Schrodinger –type equationsMathematical Problems in Engineering2011201110.1155/2010/575679 (Article ID 575679, 11 pages)
  • I.AslanApplication of the exp-function method to nonlinear lattice differential equations for multi-wave and rational solutionsMath. Meth. Appl. Sci.34201117071710
  • A.BekirA.BozExact solutions for nonlinear evolution equations using Exp-function methodPhys. Lett. A372200816191625
  • A.BekirA.C.CevikelThe tanh–coth method combined with the Riccati equation for solving nonlinear coupled equation in mathematical physicsJ. King Saud Univ. – Sci.232011127132
  • A.S.DeakinM.DavisonAnalytic solution for a vasicek interest rate convertible bond modelJournal of Applied Mathematics2010201010.1155/2010/263451 (Article ID 263451, 5 pages)
  • J.FengW.LiQ.WanUsing (G′/G)-expansion method to seek traveling wave solution of Kolmogorov–Petrovskii–Piskunov equationAppl. Math. Comput.217201158605865
  • Khaled A.GepreelAGeneralized (G′/G)-expansion method for finding trvelling wave solutions of nonlinear evolution equationsJ. Partial Differ. Equ.2420115569
  • K.A.GepreelExact solutions for nonlinear PDEs with the variable coefficients in mathematical physicsJ. Inf. Comput. Sci.612011003014
  • Khaled A.GepreelShehataExact complextion soliton solutions for nonlinear partial differential equations in mathematical physicsSci. Res. Essays722012149157 (16 January)
  • C.A.GomezA.H.SalasExact solutions for the generalized BBM equation with variable coefficientsMathematical Problems in Engineering2010201010.1155/2010/498249 (Article ID 498249, 10 pages)
  • S.GuoL.MeiY.ZhouC.LiThe extended Riccati equation mapping method for variable-coefficient diffusion-reaction and mKdV equationAppl. Math. Comput.217201162646272
  • J.H.HeSome asymptotic methods for strongly nonlinear equationInt. J. Mod. Phys.2020200611441199 (10)
  • H.HeX.H.WuExp-function method for nonlinear wave equationsChaos Soliton Fract.302006700708
  • R.HirotaExact solution of the KdV equation for multiple collisions of solutionsPhys. Rev. Lett.27197111921194
  • X.LiuL.TianY.WuApplication of (G′/G) -expansion method to two nonlinear evolution equationsAppl. Math. Comput.217201013761384
  • W.X.MaY.YouSolving the Korteweg–de Vries equation by its bilinear form: Wronskian solutionsTrans. Am. Math. Soc.357200417531778
  • W.MalflietSolitary wave solutions of nonlinear wave equationsAm. J. Phys.601992650654
  • M.MassaboR.CianciO.PaladinoAn analytical solution of the advection dispersion equation in a bounded domain and its application to laboratory experimentsJournal of Applied Mathematics2011201110.1155/2011/493014 (Article ID 493014, 14 pages)
  • S.T.Mohyud-dinM.A.NoorK.I.NoorExp-function method for traveling wave solutions of modified Zakharov–Kuznetsov equationJ. King Saud Univ.222010213216
  • H.NaherF.AbdullahM.A.AkbarThe (G′/G) -expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equationMathematical Problems in Engineering2011201110.1155/2011/218216 (Article ID 218216)
  • H.NaherF.AbdullahM.A.AkbarNew travelling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method20122012201110.1155/2012/575387 (Article ID 575387, 14 pages)
  • T.A.NofelM.SayedY.S.HamadS.K.ElaganThe improved (G′/G)-expansion method for solving the fifth-order KdV equationAnn. Fuzzy Math. Info.32011917
  • T.OzisI.AslanApplication of the (G′/G)-expansion method to Kawahara type equations using symbolic computationAppl. Math. Comput.216201023602365
  • C.RogersW.F.ShadwickBacklund Transformations1982Aca PressNew York
  • F.SalahZ.A.AzizD.L.C.ChingNew exact solutions for MHD transient rotating flow of a second-grade fluid in a porous mediumJournal of Applied Mathematics2011201110.1155/2011/823034 (Article ID 823034, 8 pages)
  • A.SalasSome solutions for a type of generalized Sawada–kotera equationAppl. Math. Comput.1962008812817
  • A.H.SalasC.A.GomezApplication of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equationMathematical Problems in Engineering2010201010.1155/2010/194329 (Article ID 194329, 14 pages)
  • A.A.SolimanH,A.AbdoNew exact Solutions of nonlinear variants of the RLW, the PHI-four and Boussinesq equations based on modified extended direct algebraic methodInt. J. Nonlinear Sci.732009274282
  • M.WangX.LiJ.ZhangThe (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physicsPhys. Lett. A3722008417423
  • A.M.WazwazThe sine–cosine method for handling nonlinear wave equationsMath. Comput. Modell.4052004499508
  • A.M.WazwazThe sine–cosine method for obtaining solutions with compact and noncompact structuresAppl. Math. Comput.15922004559576
  • A.M.WazwazThe tanh–coth method for solitons and kink solutions for nonlinear parabolic equationsAppl. Math. Comput.188200714671475
  • A.M.WazwazA new (2 + 1)-dimensional Korteweg-de-Vries equation and its extension to a new (3 + 1)-dimensional Kadomtsev–Petviashvili equationPhys. Scr.842011035010 http://dx.doi.org/10.1088/0031-8949/84/03/035010
  • A.YildirimZ.PinarApplication of the exp-function method for solving nonlinear reaction-diffusion equations arising in mathematical biologyComput. Math. Appl.60201018731880
  • B.I.YunAn iteration method generating analytical solutions for Blasius problemJournal of Applied Mathematics2011201110.1155/2011/925649 (Article ID 925649, 8 pages)
  • M.E.ZayedS.Al-JoudiApplications of an Extended (G′/G) -Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical PhysicsMathematical Problems in Engineering2010201010.1155/2010/768573 (Article ID 768573, 19 pages)
  • M.E.ZayedKhaled A.GepreelA series of complextion soliton solutions for nonlinear Jaulent-Miodek PDEs using Ricatti ezquations methodProc. R. Soc. Edinburgh, Sect. A: Math.141A201110011015
  • S.ZhangJ.BaY.SunL.DongAnalytic solutions of a (2 + 1)-dimensional variable-coefficient Broer-Kaup systemMath. Meth. Appl. Sci.201010.1002/mma.1343
  • Y.M.ZhaoY.J.YangW.LiApplication of the improved (G′/G)-expansion method for the variant Boussinesq equationsAppl. Math. Sci.558201128552861
  • S.ZhuThe generalizing Riccati equation mapping method in non-linear evolution equation: application to (2 + 1)-dimensional Boiti–Leon–Pempinelle equationChaos Soliton Fract.37200813351342

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.