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Volumn 8, Issue 2, 2008, Pages 358-363

Explicit solution of nonlinear ZK-BBM wave equation using Exp-function method

Author keywords

Benjamin Bona Mahony Burgers (BBMB) equations; Exp function method

Indexed keywords

FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; WAVE EQUATIONS;

EID: 41949085630     PISSN: 18125654     EISSN: 18125662     Source Type: Journal    
DOI: 10.3923/jas.2008.358.363     Document Type: Article
Times cited : (34)

References (33)
  • 3
    • 34547422837 scopus 로고    scopus 로고
    • Approximate explicit solutions of nonlinear BBMB equations by homotopy, analysis method and comparison with the exact solution
    • Fakhari, A., D.D. Ganji and Ebrahimpour, 2007. Approximate explicit solutions of nonlinear BBMB equations by homotopy, analysis method and comparison with the exact solution. Phys. Lett. A, 368 (1-2): 64-68.
    • (2007) Phys. Lett. A , vol.368 , Issue.1-2 , pp. 64-68
    • Fakhari, A.1    Ganji, D.D.2    Ebrahimpour3
  • 4
    • 33745244211 scopus 로고    scopus 로고
    • Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method
    • Ganji, D.D. and M. Rafei, 2006. Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method. Phys. Lett. A, 356 (2): 131-137.
    • (2006) Phys. Lett. A , vol.356 , Issue.2 , pp. 131-137
    • Ganji, D.D.1    Rafei, M.2
  • 5
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method: A kind of nonlinear analytical technique: Some examples
    • He, J.H., 1999. Variational iteration method: A kind of nonlinear analytical technique: Some examples. Int. J. Nonl. Mech., 344: 699.
    • (1999) Int. J. Nonl. Mech , vol.344 , pp. 699
    • He, J.H.1
  • 6
    • 0040184009 scopus 로고    scopus 로고
    • Variational iteration method for autonomous ordinary differential systems
    • He, J.H., 2000. Variational iteration method for autonomous ordinary differential systems. Applied Math Comput, 114 (1-2): 115.
    • (2000) Applied Math Comput , vol.114 , Issue.1-2 , pp. 115
    • He, J.H.1
  • 7
    • 0041621600 scopus 로고    scopus 로고
    • Variational principles for some nonlinear partial differential equations with variable coefficients
    • He, J.H., 2004. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons and Fractals, 19 (4): 847.
    • (2004) Chaos, Solitons and Fractals , vol.19 , Issue.4 , pp. 847
    • He, J.H.1
  • 8
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equations
    • He, J.H., 2005. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons Fractals, 26 (3): 695.
    • (2005) Chaos, Solitons Fractals , vol.26 , Issue.3 , pp. 695
    • He, J.H.1
  • 10
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • He, J.H. and X.H. Wu, 2006. Exp-function method for nonlinear wave equations. Chaos, Solitons Fractals, 30 (3): 700.
    • (2006) Chaos, Solitons Fractals , vol.30 , Issue.3 , pp. 700
    • He, J.H.1    Wu, X.H.2
  • 11
    • 0022060214 scopus 로고
    • A general physical approach to solitary wave construction from linear solutions
    • Hereman, W., A. Korpel and P.P. Banerjee, 1985. A general physical approach to solitary wave construction from linear solutions. Wave Motion, 7 (3): 283-289.
    • (1985) Wave Motion , vol.7 , Issue.3 , pp. 283-289
    • Hereman, W.1    Korpel, A.2    Banerjee, P.P.3
  • 12
    • 35949040541 scopus 로고
    • Exact solution of the Kdv equation for multiple collisions of solitons
    • Hirota, R., 1971. Exact solution of the Kdv equation for multiple collisions of solitons. Phys. Rev. Lett., 27: 1192-1194.
    • (1971) Phys. Rev. Lett , vol.27 , pp. 1192-1194
    • Hirota, R.1
  • 13
    • 4243067324 scopus 로고    scopus 로고
    • An algebraic method exactly solving two high-dimensional nonlinear evolution equations
    • Hu, J.Q., 2005. An algebraic method exactly solving two high-dimensional nonlinear evolution equations. Chaos, Solitons Fractals, 23 (2): 391.
    • (2005) Chaos, Solitons Fractals , vol.23 , Issue.2 , pp. 391
    • Hu, J.Q.1
  • 14
    • 0000262859 scopus 로고
    • On the stability of solitary waves in weakly dispersive media
    • Kadomtsev, B.B. and V.I. Petviashvili, 1970. On the stability of solitary waves in weakly dispersive media. Sov. Phys. Dokl., 15: 539-541.
    • (1970) Sov. Phys. Dokl , vol.15 , pp. 539-541
    • Kadomtsev, B.B.1    Petviashvili, V.I.2
  • 15
    • 0041736716 scopus 로고    scopus 로고
    • Exact travelling wave solutions for Kuznetsov equation
    • Li, B., Y. Chen and H. Zhang, 2003. Exact travelling wave solutions for Kuznetsov equation. Applied Math. Comput, 146 (1-2): 653-666.
    • (2003) Applied Math. Comput , vol.146 , Issue.1-2 , pp. 653-666
    • Li, B.1    Chen, Y.2    Zhang, H.3
  • 16
    • 0035828886 scopus 로고    scopus 로고
    • Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
    • Liu, S.K., Z.T. Fu, S.D. Liu and Q. Zhao, 2001. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys. Lett. A, 289 (1-2): 69-74.
    • (2001) Phys. Lett. A , vol.289 , Issue.1-2 , pp. 69-74
    • Liu, S.K.1    Fu, Z.T.2    Liu, S.D.3    Zhao, Q.4
  • 17
    • 0001229736 scopus 로고
    • Solitary wave solutions of nonlinear wave equations
    • Malfliet, W., 1992. Solitary wave solutions of nonlinear wave equations. Am. J. Phys., 60 (7): 650-654.
    • (1992) Am. J. Phys , vol.60 , Issue.7 , pp. 650-654
    • Malfliet, W.1
  • 18
    • 0000068096 scopus 로고    scopus 로고
    • The Tanh Method: II. Perturbation technique for conservative systems
    • Malfliet, W. and W. Hereman, 1996. The Tanh Method: II. Perturbation technique for conservative systems, Phys. Ser., 54: 569-575.
    • (1996) Phys. Ser , vol.54 , pp. 569-575
    • Malfliet, W.1    Hereman, W.2
  • 19
    • 0001078296 scopus 로고    scopus 로고
    • The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions
    • Monro, S. and E.J. Parkes, 1999. The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions. J. Plasma Phys., 62 (3): 305-317.
    • (1999) J. Plasma Phys , vol.62 , Issue.3 , pp. 305-317
    • Monro, S.1    Parkes, E.J.2
  • 20
    • 33745965279 scopus 로고    scopus 로고
    • Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method
    • Rafei, M. and D.D. Ganji, 2006. Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method. Int J. Nonl. Sci. Numer. Simul. 7 (3): 321-328.
    • (2006) Int J. Nonl. Sci. Numer. Simul , vol.7 , Issue.3 , pp. 321-328
    • Rafei, M.1    Ganji, D.D.2
  • 21
    • 12044253199 scopus 로고
    • Compactons: Solitons with finite wavelengths
    • Rosenau, P. and J.M. Hyman, 1993. Compactons: Solitons with finite wavelengths. Phys. Rev. Lett., 70 (5): 564-567.
    • (1993) Phys. Rev. Lett , vol.70 , Issue.5 , pp. 564-567
    • Rosenau, P.1    Hyman, J.M.2
  • 22
    • 34347345899 scopus 로고    scopus 로고
    • Approximate explicit solutions of nonlinear BBMB equations by He's methods and comparison with the exact solution
    • Tari, H. and D.D. Ganji, 2007. Approximate explicit solutions of nonlinear BBMB equations by He's methods and comparison with the exact solution. Phys. Lett. A, 367 (1-2): 95-101.
    • (2007) Phys. Lett. A , vol.367 , Issue.1-2 , pp. 95-101
    • Tari, H.1    Ganji, D.D.2
  • 23
    • 41149140086 scopus 로고    scopus 로고
    • Tolou, N., D.D. Ganji, M.J. Hosseini and Z.Z. Ganji, 2007. Application of Homotopy Perturbation Method in Nonlinear Heat Diffusion-Convection-Reaction. Equations. Open Mech. J., 1: 20-25.
    • Tolou, N., D.D. Ganji, M.J. Hosseini and Z.Z. Ganji, 2007. Application of Homotopy Perturbation Method in Nonlinear Heat Diffusion-Convection-Reaction. Equations. Open Mech. J., 1: 20-25.
  • 24
    • 0001051423 scopus 로고    scopus 로고
    • Exact solutions for a compound KdV-Burgers equation
    • Wang, L., 1996. Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A, 213 (5-6): 279-287.
    • (1996) Phys. Lett. A , vol.213 , Issue.5-6 , pp. 279-287
    • Wang, L.1
  • 26
    • 0001762098 scopus 로고
    • On three-dimensional solitons
    • Zakharov,, V.E. and E.A. Kuznetsov, 1974. On three-dimensional solitons. Soviet Phys., 39 (1): 285-288.
    • (1974) Soviet Phys , vol.39 , Issue.1 , pp. 285-288
    • Zakharov, V.E.1    Kuznetsov, E.A.2
  • 27
    • 7244223299 scopus 로고    scopus 로고
    • Group analysis and midified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear euler equations
    • Zayed, E.M.E., H.A. Zedan and K.A. Gepreel, 2004. Group analysis and midified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear euler equations. Int. J. Nonl. Sci. Numer. Simul., 5 (1): 221.
    • (2004) Int. J. Nonl. Sci. Numer. Simul , vol.5 , Issue.1 , pp. 221
    • Zayed, E.M.E.1    Zedan, H.A.2    Gepreel, K.A.3
  • 28
    • 33749514277 scopus 로고    scopus 로고
    • Symbolic computation and new families of exact non-travelling wave solutions to (3+1)-dimensional Kadomstev-Petviashvili equation
    • Zhang, S. and T.C. Xia, 2006a. Symbolic computation and new families of exact non-travelling wave solutions to (3+1)-dimensional Kadomstev-Petviashvili equation. Applied Math. Comput., 181 (1): 319-331.
    • (2006) Applied Math. Comput , vol.181 , Issue.1 , pp. 319-331
    • Zhang, S.1    Xia, T.C.2
  • 29
    • 33751516044 scopus 로고    scopus 로고
    • Further improved extended Fan sub-equation method and new exact solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equations
    • Zhang, S. and T.C. Xia, 2006b. Further improved extended Fan sub-equation method and new exact solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equations. Applied Math. Comput., 182 (2): 1651-1660.
    • (2006) Applied Math. Comput , vol.182 , Issue.2 , pp. 1651-1660
    • Zhang, S.1    Xia, T.C.2
  • 30
    • 33748193665 scopus 로고    scopus 로고
    • New exact solutions of the KdV-Burgers-Kuramoto equation
    • Zhang, S., 2006. New exact solutions of the KdV-Burgers-Kuramoto equation. Phys. Lett. A, 358 (5-6): 414-420.
    • (2006) Phys. Lett. A , vol.358 , Issue.5-6 , pp. 414-420
    • Zhang, S.1
  • 31
    • 33747366968 scopus 로고    scopus 로고
    • Symbolic computation and new families of exact non-travelling wave solutions of (2+1)-dimensional Konopelchenko-Dubrovsky equations
    • Zhang, S., 2007a. Symbolic computation and new families of exact non-travelling wave solutions of (2+1)-dimensional Konopelchenko-Dubrovsky equations. Chaos, Solitons and Fractals, 31 (4): 951-959.
    • (2007) Chaos, Solitons and Fractals , vol.31 , Issue.4 , pp. 951-959
    • Zhang, S.1
  • 32
    • 33845455039 scopus 로고    scopus 로고
    • Further improved F-expansion method and new exact solutions of Kadomstev-Petviashvili Equation
    • Zhang, S., 2007b. Further improved F-expansion method and new exact solutions of Kadomstev-Petviashvili Equation. Chaos, Solitons Fractals, 32 (4): 1375-1383.
    • (2007) Chaos, Solitons Fractals , vol.32 , Issue.4 , pp. 1375-1383
    • Zhang, S.1
  • 33
    • 27144487394 scopus 로고    scopus 로고
    • Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system
    • Zhao, X.Q., H.Y. Zhi and H.Q. Zhang, 2006. Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system. Chaos Solitons Fractals, 28 (1): 112-126.
    • (2006) Chaos Solitons Fractals , vol.28 , Issue.1 , pp. 112-126
    • Zhao, X.Q.1    Zhi, H.Y.2    Zhang, H.Q.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.