Approximate solutions for solving the Klein–Gordon and sine-Gordon equationsFootnote

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References

• S.AbbasbandyNumerical solution of non-linear Klein–Gordon equations by variational iteration methodInt. J. Numer. Methods Eng.702007876881
   Web of Science ®Google Scholar
• B.BatihaMSMNooraniI.HashimNumerical solution of sine-Gordon equation by variational iteration methodJ. Phys. Lett. A3702007437440
   Google Scholar
• J.BiazarF.MohammadiApplication of differential transform method to the sine-Gordon equationInt. J. Nonlinear Sci.102010190195
   Google Scholar
• J.BiazarE.MostafaAnalytical solution of the Klein–Gordon equation by a new homotopy perturbation methodComput. Math. Model.252014124134
   Google Scholar
• JingChenJieYangHongxiangYangSingle soliton solutions of the coupled nonlinear Klein–Gordon equations with power law nonlinearityAppl. Math. Comput.2462014184191
   Google Scholar
• M.S.H.ChowdhuryI.HashimApplication of homotopy-perturbation method to Klein–Gordon and sine-Gordon equationsJ. Chaos Solitons Fractals39200919281935
   Web of Science ®Google Scholar
• D.KayaA numerical solution of the sine-Gordon equation using the modified decomposition methodAppl. Math. Comput.1432003309317
   Google Scholar
• MehdiDehghanMostafaAbbaszadehAkbarMohebbiAn implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein–Gordon equationsEng. Anal. Boundary Elem.502015412434
   Web of Science ®Google Scholar
• Y.ElcinThe variational iteration method for studying the Klein Gordon equationJ. Appl. Math. Lett.212008669674
   Google Scholar
• S.M.El-SayedThe decomposition method for studying the Klein–Gordon equationJ. Chaos Solitons Fractals18200310251030
   Google Scholar
• H.FadhilA.SaadA.BewarA.MajeedVariational homotopy perturbation method for solving Benjamin–Bona–Mahony EquationAppl. Math. (AM)62015675683
   Google Scholar
• Y.FukangT.TianS.JunqiangMinZhuSpectral methods using Legendre wavelets for nonlinear Klein/Sine-Gordon equationsJ. Comput. Appl. Math.2752015321334
   Google Scholar
• ShiminGuoLiquanMeiThe fractional variational iteration method using Hes polynomialsPhys. Lett. A3752011309313
   Google Scholar
• ShiminGuoLiquanMeiYingLiFractional variational homotopy perturbation iteration method and its application to a fractional diffusion equationAppl. Math. Comput.219201359095917
   Web of Science ®Google Scholar
• J.H.HeHomotopy perturbation techniqueJ. Comput. Methods Appl. Mech. Eng.1781999257262
   Web of Science ®Google Scholar
• J.H.HeVariational iteration method a kind of non-linear analytical technique: some examplesInt. J. Nonlinear Mech.341999699708
   Web of Science ®Google Scholar
• M.MatinfarM.GhasemiVariational homotopy perturbation method for the Zakharove–Kuznetsov equationsJ. Math. Stat.62010425430
   Google Scholar
• M.MatinfarZ.RaeisiM.MahdaviVariational homotopy perturbation method for the fishers equationInt. J. Nonlinear Sci.92010374378
   Google Scholar
• A.N.MuhammadT.M.SyedVariational homotopy perturbation method for solving higher dimensional initial boundary value problemsJ. Math. Prob. Eng.2008 Article ID 696734
   Google Scholar
• A.S.V.Ravi KanthK.ArunaDifferential transform method for solving the linear and nonlinear Klein–Gordon equationJ. Comput. Phys. Commun.1802009708711
   Web of Science ®Google Scholar
• Mourad S.SemaryHany N.HassanA new approach for a class of nonlinear boundary value problems with multiple solutionsJ. Assoc. Arab Univ. Basic Appl. Sci.1720152735
   Google Scholar
• A.M.WazwazThe tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein–Gordon equationJ. Appl. Math. Comput.167200511791195
   Google Scholar
• A.M.YangY.Z.ZhangC.CattaniG.N.XieM.M.RashidiY.J.ZhouX.J.YangApplication of local fractional series expansion method to solve Klein–Gordon equations on cantor setsAbstract Appl. Anal.20142014 Article ID 37274
   Google Scholar
• Elsayed M.E.ZayedHanan M.Abdel RahmanOn solving the KdV-Burgers equation and the Wu-Zhang equations using the modified variational iteration methodInt. J. Nonlinear Sci. Numer. Simul.10200910931103
   Google Scholar
• Elsayed M.E.ZayedHanan M.Abdel RahmanOn using the modified variational iteration method for solving the nonlinear coupled equations in the mathematical physicsRicerche Mat592010137159
   Google Scholar
• Elsayed M.E.ZayedHanan M.Abdel RahmanThe Variational iteration method and the variational homotopy perturbation method for solving the KdV-Burger’s equation and the Sharma–Tasso–Olver equationZeitschrift fur Naturforschung65a20102533
   Google Scholar
• XueqinZhaoHongyanZhiYaxuanYuHongqingZhangA new Riccati equation expansion method with symbolic computation to construct new travelling wave solution of nonlinear differential equationsJ. Appl. Math. Comput.17220062439
   Google Scholar