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Volumn 22, Issue 3, 2012, Pages 317-331

Exact solutions of shallow water wave equations by using the (G′/G)-expansion method

Author keywords

[No Author keywords available]

Indexed keywords

EXACT SOLUTION; EXPANSION METHODS; NONLINEAR EVOLUTION EQUATION; NONLINEAR WAVE EQUATION; SHALLOW WATER WAVE EQUATION; TRAVELLING WAVE SOLUTION; TRIGONOMETRIC FUNCTIONS;

EID: 84864764724     PISSN: 17455030     EISSN: 17455049     Source Type: Journal    
DOI: 10.1080/17455030.2012.683890     Document Type: Article
Times cited : (36)

References (42)
  • 2
    • 0037411678 scopus 로고    scopus 로고
    • A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation
    • V.O. Vakhnenko, E.J. Parkes, and A.J. Morrison, A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos, Solitons Fractals 17 (2003), p. 683.
    • (2003) Chaos, Solitons Fractals , vol.17 , pp. 683
    • Vakhnenko, V.O.1    Parkes, E.J.2    Morrison, A.J.3
  • 3
    • 0013052570 scopus 로고
    • Direct method of finding exact solutions of nonlinear evolution equations
    • R. Bullough and P. Caudrey, eds., Springer, Berlin
    • R. Hirota, Direct method of finding exact solutions of nonlinear evolution equations, in Backlund Transformations, R. Bullough and P. Caudrey, eds., Springer, Berlin, 1980, p. 1157.
    • (1980) Backlund Transformations , pp. 1157
    • Hirota, R.1
  • 4
    • 44649179317 scopus 로고    scopus 로고
    • Multiple-soliton solutions of two extended model equations for shallow water waves
    • A.M. Wazwaz, Multiple-soliton solutions of two extended model equations for shallow water waves, Appl. Math. Comput. 201 (2008), p. 790.
    • (2008) Appl. Math. Comput. , vol.201 , pp. 790
    • Wazwaz, A.M.1
  • 5
    • 0004483962 scopus 로고    scopus 로고
    • The tanh method. I: Exact solutions of nonlinear evolution and wave equations
    • W. Malfliet and W. Hereman, The tanh method. I: Exact solutions of nonlinear evolution and wave equations, Physica Scripta 54 (1996), p. 563.
    • (1996) Physica Scripta , vol.54 , pp. 563
    • Malfliet, W.1    Hereman, W.2
  • 6
    • 55149084798 scopus 로고    scopus 로고
    • Extended improved tanh-function method for solving the nonlinear physical problems
    • A.A. Soliman, Extended improved tanh-function method for solving the nonlinear physical problems, Acta Applicandae Mathematicae 104 (2008), p. 367.
    • (2008) Acta Applicandae Mathematicae , vol.104 , pp. 367
    • Soliman, A.A.1
  • 7
    • 0034606149 scopus 로고    scopus 로고
    • Extended tanh-function method and its applications to nonlinear equations
    • E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277 (2000), p. 212.
    • (2000) Phys. Lett. A , vol.277 , pp. 212
    • Fan, E.1
  • 8
    • 33747348716 scopus 로고    scopus 로고
    • New exact travelling wave solutions using modified extended tanh-function method
    • S.A. El-Wakil and M.A. Abdou, New exact travelling wave solutions using modified extended tanh-function method, Chaos, Solitons Fractals 31 (2007), p. 840.
    • (2007) Chaos, Solitons Fractals , vol.31 , pp. 840
    • El-Wakil, S.A.1    Abdou, M.A.2
  • 9
    • 12944300203 scopus 로고    scopus 로고
    • A sine-cosine method for handling nonlinear wave equations
    • A.M. Wazwaz, A sine-cosine method for handling nonlinear wave equations, Math. Comput. Model. 40 (2004), p. 499.
    • (2004) Math. Comput. Model. , vol.40 , pp. 499
    • Wazwaz, A.M.1
  • 10
    • 43249113201 scopus 로고    scopus 로고
    • New solitons and periodic wave solutions for some nonlinear physical models by using sine-cosine method
    • A. Bekir, New solitons and periodic wave solutions for some nonlinear physical models by using sine-cosine method, Physica Scripta 77 (2008), p. 501.
    • (2008) Physica Scripta , vol.77 , pp. 501
    • Bekir, A.1
  • 11
    • 4344673183 scopus 로고    scopus 로고
    • A note on the homogeneous balance method
    • E. Fan and H. Zhang, A note on the homogeneous balance method, Phys. Lett. A 246 (1998), p. 403.
    • (1998) Phys. Lett. A , vol.246 , pp. 403
    • Fan, E.1    Zhang, H.2
  • 12
    • 0001051423 scopus 로고    scopus 로고
    • Exact solutions for a compound KdV-Burgers equation
    • M.L. Wang, Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A 213 (1996), p. 279.
    • (1996) Phys. Lett. A , vol.213 , pp. 279
    • Wang, M.L.1
  • 13
    • 24344489016 scopus 로고    scopus 로고
    • Jacobian elliptic function method for nonlinear differentialdifference equations
    • C.Q. Dai and J.F. Zhang, Jacobian elliptic function method for nonlinear differentialdifference equations, Chaos, Solitons Fractals 27 (2006), p. 1042.
    • (2006) Chaos, Solitons Fractals , vol.27 , pp. 1042
    • Dai, C.Q.1    Zhang, J.F.2
  • 14
    • 0035828886 scopus 로고    scopus 로고
    • Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
    • S. Liu, Z. Fu, S. Liu, and Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Phys. Lett. A 289 (2001), p. 69.
    • (2001) Phys. Lett. A , vol.289 , pp. 69
    • Liu, S.1    Fu, Z.2    Liu, S.3    Zhao, Q.4
  • 15
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • J.H. He and X.H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons Fractals 30 (2006), p. 700.
    • (2006) Chaos, Solitons Fractals , vol.30 , pp. 700
    • He, J.H.1    Wu, X.H.2
  • 16
    • 55549089262 scopus 로고    scopus 로고
    • Exact and explicit solutions to the (3+1)-dimensional Jimbo-Miwa equation via the Exp-function method
    • T. Ozis and I. Aslan, Exact and explicit solutions to the (3+1)-dimensional Jimbo-Miwa equation via the Exp-function method, Phys. Lett. A 372 (2008), p. 7011.
    • (2008) Phys. Lett. A , vol.372 , pp. 7011
    • Ozis, T.1    Aslan, I.2
  • 17
    • 58449110860 scopus 로고    scopus 로고
    • The exp-function method for the Riccati equation and exact solutions of dispersive long wave equations
    • S. Zhang, W. Wang, and J.-L. Tong, The exp-function method for the Riccati equation and exact solutions of dispersive long wave equations, Z. Naturforsch. 63a (2008), p. 663.
    • (2008) Z. Naturforsch. , vol.63 , pp. 663
    • Zhang, S.1    Wang, W.2    Tong, J.-L.3
  • 18
    • 77955943505 scopus 로고    scopus 로고
    • Exp-function method for generalized travelling solutions of Calogero-Degasperis-Fokas equation
    • S.T. Mohyud-Din, M.A. Noor, and A. Waheed, Exp-function method for generalized travelling solutions of Calogero-Degasperis-Fokas equation, Zeitschrift für Naturforschung 65a (2010), p. 78.
    • (2010) Zeitschrift für Naturforschung , vol.65 , pp. 78
    • Mohyud-Din, S.T.1    Noor, M.A.2    Waheed, A.3
  • 19
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equation
    • J.H. He, Some asymptotic methods for strongly nonlinear equation, Int. J. Mod. Phys. 20 (2006), p. 1144.
    • (2006) Int. J. Mod. Phys. , vol.20 , pp. 1144
    • He, J.H.1
  • 20
    • 68949122726 scopus 로고    scopus 로고
    • Some relatively new techniques for nonlinear problems
    • 234849
    • S.T. Mohyud-Din, M.A. Noor, and K.I. Noor, Some relatively new techniques for nonlinear problems, Math. Probl. Eng. 234849 (2009), p. 25.
    • (2009) Math. Probl. Eng. , pp. 25
    • Mohyud-Din, S.T.1    Noor, M.A.2    Noor, K.I.3
  • 21
    • 77951248176 scopus 로고    scopus 로고
    • Analytical approach to fractional partial differential equations in fluid mechanics by means of the homotopy perturbation method
    • A. Yildirim, Analytical approach to fractional partial differential equations in fluid mechanics by means of the homotopy perturbation method, Int. J. Numer. Meth. Heat Fluid Flow 20 (2010), p. 186.
    • (2010) Int. J. Numer. Meth. Heat Fluid Flow , vol.20 , pp. 186
    • Yildirim, A.1
  • 22
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method - A kind of non-linear analytical technique: Some examples
    • J.H. He, Variational iteration method - A kind of non-linear analytical technique: Some examples, Int. J. Nonlin. Mech. 34 (1999), p. 699.
    • (1999) Int. J. Nonlin. Mech. , vol.34 , pp. 699
    • He, J.H.1
  • 23
    • 43749107936 scopus 로고    scopus 로고
    • Variational iteration method for solving higher-order nonlinear boundary value problems using He's polynomials
    • M.A. Noor and S.T. Mohyud-Din, Variational iteration method for solving higher-order nonlinear boundary value problems using He's polynomials, Int. J. Nonlin. Sci. Num. Simul. 9 (2008), p. 141.
    • (2008) Int. J. Nonlin. Sci. Num. Simul. , vol.9 , pp. 141
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 24
    • 77955941033 scopus 로고    scopus 로고
    • Application of He's variational iteration method to nonlinear integrodifferential equations
    • A. Yldrm, Application of He's variational iteration method to nonlinear integrodifferential equations, Zeitschrift für Naturforschung A 65a (2010), p. 418.
    • (2010) Zeitschrift für Naturforschung A , vol.65 A , pp. 418
    • Yldrm, A.1
  • 25
    • 37549033511 scopus 로고    scopus 로고
    • The (G'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
    • M.L. 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 (2008), p. 417.
    • (2008) Phys. Lett. A , vol.372 , pp. 417
    • Wang, M.L.1    Li, X.2    Zhang, J.3
  • 26
    • 39849101219 scopus 로고    scopus 로고
    • A generalized (G'/G)-expansion method for the mKdV equation with variable coefficients
    • S. Zhang, J.-L. Tong, and W. Wang, A generalized (G'/G)-expansion method for the mKdV equation with variable coefficients, Phys. Lett. A 372 (2008), p. 2254.
    • (2008) Phys. Lett. A , vol.372 , pp. 2254
    • Zhang, S.1    Tong, J.-L.2    Wang, W.3
  • 27
    • 41949137395 scopus 로고    scopus 로고
    • Application of the (G'/G)-expansion method for nonlinear evolution equations
    • A. Bekir, Application of the (G'/G)-expansion method for nonlinear evolution equations, Phys. Lett. A 372 (2008), p. 3400.
    • (2008) Phys. Lett. A , vol.372 , pp. 3400
    • Bekir, A.1
  • 28
    • 60349094795 scopus 로고    scopus 로고
    • Analytic study on two nonlinear evolution equations by using the (G'/G)- expansion method
    • I. Aslan and T. Ozis, Analytic study on two nonlinear evolution equations by using the (G'/G)- expansion method, Appl. Math. Comput. 209 (2009), p. 425.
    • (2009) Appl. Math. Comput. , vol.209 , pp. 425
    • Aslan, I.1    Ozis, T.2
  • 29
    • 59349118015 scopus 로고    scopus 로고
    • The (G'/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics
    • E.M.E. Zayed and K.A. Gepreel, The (G'/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics, J. Math. Phys. 50 (2009), 013502.
    • (2009) J. Math. Phys. , vol.50 , pp. 013502
    • Zayed, E.M.E.1    Gepreel, K.A.2
  • 30
    • 79958804512 scopus 로고    scopus 로고
    • Application of the (G'/G)-expansion method for the Burgers, Burgers-Huxley and modified Burgers-KdV equations
    • H. Kheiri, M.R. Moghaddan, and V. Vafaei, Application of the (G'/G)-expansion method for the Burgers, Burgers-Huxley and modified Burgers-KdV equations, Pramana J. Phys. 76 (2011), p. 831.
    • (2011) Pramana J. Phys. , vol.76 , pp. 831
    • Kheiri, H.1    Moghaddan, M.R.2    Vafaei, V.3
  • 31
    • 77949534972 scopus 로고    scopus 로고
    • The (G'/G)-expansion method for a discrete nonlinear Schrödinger equation
    • S. Zhang, L. Dong, J.-M. Ba, and Y.-N. Sun, The (G'/G)-expansion method for a discrete nonlinear Schrödinger equation, Pramana J. Phys. 74 (2010), p. 207.
    • (2010) Pramana J. Phys. , vol.74 , pp. 207
    • Zhang, S.1    Dong, L.2    Ba, J.-M.3    Sun, Y.-N.4
  • 32
    • 77949490735 scopus 로고    scopus 로고
    • Travelling wave solutions for time-delayed nonlinear evolution equations
    • H. Kim and R. Sakthivel, Travelling wave solutions for time-delayed nonlinear evolution equations, Appl. Math. Lett. 23 (2010), p. 527.
    • (2010) Appl. Math. Lett. , vol.23 , pp. 527
    • Kim, H.1    Sakthivel, R.2
  • 33
    • 79957495137 scopus 로고    scopus 로고
    • New variable separation solutions of two-dimensional Burgers system
    • Y. Gurefe and E. M|s|rl|, New variable separation solutions of two-dimensional Burgers system, Appl. Math. Comput. 217 (2011), p. 9189.
    • (2011) Appl. Math. Comput. , vol.217 , pp. 9189
    • Gurefe, Y.1    Msrl, E.2
  • 34
    • 79953750833 scopus 로고    scopus 로고
    • Application of (G'/G)-expansion method to Regularized Long Wave (RLW) equation
    • M.M. Kabir, A. Borhanifar, and R. Abazari, Application of (G'/G)-expansion method to Regularized Long Wave (RLW) equation, Comput. Math. Appl. 61 (2011), p. 2044.
    • (2011) Comput. Math. Appl. , vol.61 , pp. 2044
    • Kabir, M.M.1    Borhanifar, A.2    Abazari, R.3
  • 35
    • 70350217177 scopus 로고    scopus 로고
    • (G'/G)-expansion method equivalent to extended tanh function method
    • C.P. Liu, (G'/G)-expansion method equivalent to extended tanh function method, Commun. Theor. Phys. (Beijing, China) 51 (2009), p. 985.
    • (2009) Commun. Theor. Phys. (Beijing, China) , vol.51 , pp. 985
    • Liu, C.P.1
  • 36
    • 77957259182 scopus 로고    scopus 로고
    • Observations on the basic (G'/G)-expansion method for finding solutions to nonlinear evolution equations
    • E.J. Parkes, Observations on the basic (G'/G)-expansion method for finding solutions to nonlinear evolution equations, Appl. Math. Comput. 217 (2010), p. 1759.
    • (2010) Appl. Math. Comput. , vol.217 , pp. 1759
    • Parkes, E.J.1
  • 38
    • 79957944561 scopus 로고    scopus 로고
    • Soliton solutions and conservation laws of the Gilson-Pickering equation
    • G. Ebadi, A.H. Kara, M.D. Petkovic, and A. Biswas, Soliton solutions and conservation laws of the Gilson-Pickering equation, Waves Random Complex Media 21 (2011), p. 378.
    • (2011) Waves Random Complex Media , vol.21 , pp. 378
    • Ebadi, G.1    Kara, A.H.2    Petkovic, M.D.3    Biswas, A.4
  • 39
    • 0000174288 scopus 로고
    • On a shallow water wave equation
    • P.A. Clarkson and E.L. Mansfield, On a shallow water wave equation, Nonlinearity 7 (1994), p. 975.
    • (1994) Nonlinearity , vol.7 , pp. 975
    • Clarkson, P.A.1    Mansfield, E.L.2
  • 40
    • 64849094924 scopus 로고    scopus 로고
    • Multiple soliton solutions and multiple-singular soliton solutions for two higher-dimensional shallow water wave equations
    • A.M. Wazwaz, Multiple soliton solutions and multiple-singular soliton solutions for two higher-dimensional shallow water wave equations, Appl. Math. Comput. 211 (2009), p. 495.
    • (2009) Appl. Math. Comput. , vol.211 , pp. 495
    • Wazwaz, A.M.1
  • 41
    • 67651014455 scopus 로고    scopus 로고
    • Multiple soliton solutions and multiple-singular soliton solutions for (2+1)- dimensional shallow water wave equations
    • A.M. Wazwaz, Multiple soliton solutions and multiple-singular soliton solutions for (2+1)- dimensional shallow water wave equations, Phys. Lett. A 373 (2009), p. 2927.
    • (2009) Phys. Lett. A , vol.373 , pp. 2927
    • Wazwaz, A.M.1
  • 42
    • 80054815806 scopus 로고    scopus 로고
    • Multiple-soliton solutions for extended shallow water wave equations Studies
    • A.M. Wazwaz, Multiple-soliton solutions for extended shallow water wave equations, Studies Math. Sci. 1 (2010), p. 21.
    • (2010) Math. Sci. , vol.1 , pp. 21
    • Wazwaz, A.M.1


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