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Volumn 8, Issue 5, 2013, Pages

Generalized and Improved (G′/G)-Expansion Method for (3+1)-Dimensional Modified KdV-Zakharov-Kuznetsev Equation

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPUTER PROGRAM; KDV ZAKHAROV KUZNETSEV EQUATION; MATHEMATICAL ANALYSIS; MATHEMATICAL PARAMETERS; NONLINEAR PARTIAL DIFFERENTIAL EQUATION; NONLINEAR SYSTEM;

EID: 84878538968     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0064618     Document Type: Article
Times cited : (49)

References (42)
  • 5
    • 0000607676 scopus 로고
    • Exact solutions of the generalized Kuramoto-Sivashinsky equation
    • Kudryashov NA, (1990) Exact solutions of the generalized Kuramoto-Sivashinsky equation. Physics Letters A 147: 287-291.
    • (1990) Physics Letters A , vol.147 , pp. 287-291
    • Kudryashov, N.A.1
  • 6
    • 35949040541 scopus 로고
    • Exact solution of the Korteweg-de-Vries equation for multiple collisions of solutions
    • Hirota R, (1971) Exact solution of the Korteweg-de-Vries equation for multiple collisions of solutions. Physical Review Letters 27: 1192-1194.
    • (1971) Physical Review Letters , vol.27 , pp. 1192-1194
    • Hirota, R.1
  • 7
    • 0035828886 scopus 로고    scopus 로고
    • Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
    • Liu S, Fu Z, Liu S, Zhao Q, (2001) Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A 289: 69-74.
    • (2001) Physics Letters A , vol.289 , pp. 69-74
    • Liu, S.1    Fu, Z.2    Liu, S.3    Zhao, Q.4
  • 8
    • 12244261648 scopus 로고    scopus 로고
    • Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1+1)-dimensional dispersive long wave equation
    • Chen Y, Wang Q, (2005) Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1+1)-dimensional dispersive long wave equation. Chaos, Solitons and Fractals 24: 745-757.
    • (2005) Chaos, Solitons and Fractals , vol.24 , pp. 745-757
    • Chen, Y.1    Wang, Q.2
  • 9
    • 13444278927 scopus 로고    scopus 로고
    • Jacobi elliptic function solutions for two variant Boussinesq equations
    • Lu D, (2005) Jacobi elliptic function solutions for two variant Boussinesq equations. Chaos, Solitons and Fractals 24: 1373-1385.
    • (2005) Chaos, Solitons and Fractals , vol.24 , pp. 1373-1385
    • Lu, D.1
  • 10
    • 4243528488 scopus 로고    scopus 로고
    • New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water
    • Yan Z, Zhang HQ, (2001) New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. Physics Letters A 285: 355-362.
    • (2001) Physics Letters A , vol.285 , pp. 355-362
    • Yan, Z.1    Zhang, H.Q.2
  • 11
    • 0001229736 scopus 로고
    • Solitary wave solutions of nonlinear wave equations
    • Malfliet W, (1992) Solitary wave solutions of nonlinear wave equations. American Journal of Physics 60: 650-654.
    • (1992) American Journal of Physics , vol.60 , pp. 650-654
    • Malfliet, W.1
  • 12
    • 34248229664 scopus 로고    scopus 로고
    • The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
    • Wazwaz AM, (2007) The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. Applied Mathematics and Computation 188: 1467-1475.
    • (2007) Applied Mathematics and Computation , vol.188 , pp. 1467-1475
    • Wazwaz, A.M.1
  • 13
    • 56049127915 scopus 로고    scopus 로고
    • Solitary wave solutions of two nonlinear physical models by tanh-coth method
    • Bekir A Cevikel AC, (2009) Solitary wave solutions of two nonlinear physical models by tanh-coth method. Commun Nonlinear Sci Numer Simulat 14: 1804-1809.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 1804-1809
    • Bekir, A.1    Cevikel, A.C.2
  • 14
    • 13444310842 scopus 로고    scopus 로고
    • Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation
    • Wang ML, Li XZ, (2005) Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos, Solitons and Fractals 24: 1257-1268.
    • (2005) Chaos, Solitons and Fractals , vol.24 , pp. 1257-1268
    • Wang, M.L.1    Li, X.Z.2
  • 15
    • 33745810605 scopus 로고    scopus 로고
    • The extended F-expansion method and its application for a class of nonlinear evolution equations
    • Abdou MA, (2007) The extended F-expansion method and its application for a class of nonlinear evolution equations. Chaos, Solitons and Fractals 31: 95-104.
    • (2007) Chaos, Solitons and Fractals , vol.31 , pp. 95-104
    • Abdou, M.A.1
  • 16
    • 69249236885 scopus 로고    scopus 로고
    • New exact Solutions of nonlinear variants of the RLW, the PHI-four and Boussinesq equations based on modified extended direct algebraic method
    • Soliman AA, Abdou HA, (2009) New exact Solutions of nonlinear variants of the RLW, the PHI-four and Boussinesq equations based on modified extended direct algebraic method. International Journal of Nonlinear Science 7: 274-282.
    • (2009) International Journal of Nonlinear Science , vol.7 , pp. 274-282
    • Soliman, A.A.1    Abdou, H.A.2
  • 17
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • He JH, Wu XH, (2006) Exp-function method for nonlinear wave equations. Chaos Solitons and Fractals 30: 700-708.
    • (2006) Chaos Solitons and Fractals , vol.30 , pp. 700-708
    • He, J.H.1    Wu, X.H.2
  • 18
    • 84858140930 scopus 로고    scopus 로고
    • New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method
    • Article ID: 575387, doi: 10.1155/2012/575387
    • Naher H, Abdullah FA, Akbar MA (2012) New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method. Journal of Applied Mathematics, Article ID: 575387, 14 pages, doi: 10.1155/2012/575387.
    • (2012) Journal of Applied Mathematics , pp. 14
    • Naher, H.1    Abdullah, F.A.2    Akbar, M.A.3
  • 19
    • 79956343059 scopus 로고    scopus 로고
    • Exp-function method for traveling wave solutions of modified Zakharov-Kuznetsov equation
    • Mohyud-Din ST, Noor MA, Noor KI, (2010) Exp-function method for traveling wave solutions of modified Zakharov-Kuznetsov equation. Journal of King Saud University. 22: 213-216.
    • (2010) Journal of King Saud University , vol.22 , pp. 213-216
    • Mohyud-Din, S.T.1    Noor, M.A.2    Noor, K.I.3
  • 20
    • 81855187220 scopus 로고    scopus 로고
    • The exp-function method for new exact solutions of the nonlinear partial differential equations
    • Naher H, Abdullah FA, Akbar MA, (2011) The exp-function method for new exact solutions of the nonlinear partial differential equations. International Journal of the Physical Sciences 6: 6706-6716.
    • (2011) International Journal of the Physical Sciences , vol.6 , pp. 6706-6716
    • Naher, H.1    Abdullah, F.A.2    Akbar, M.A.3
  • 21
    • 77957926102 scopus 로고    scopus 로고
    • Application of the exp-function method for solving nonlinear reaction-diffusion equations arising in mathematical biology
    • Yildirim A, Pinar Z, (2010) Application of the exp-function method for solving nonlinear reaction-diffusion equations arising in mathematical biology. Computers & Mathematics with Applications 60: 1873-1880.
    • (2010) Computers & Mathematics with Applications , vol.60 , pp. 1873-1880
    • Yildirim, A.1    Pinar, Z.2
  • 22
    • 80052266360 scopus 로고    scopus 로고
    • Application of the exp-function method to nonlinear lattice differential equations for multi-wave and rational solutions
    • Doi: 10.1002/mma.1476
    • Aslan I (2011) Application of the exp-function method to nonlinear lattice differential equations for multi-wave and rational solutions. Mathematical Methods in the Applied Sciences, Doi: 10.1002/mma.1476.
    • (2011) Mathematical Methods in the Applied Sciences
    • Aslan, I.1
  • 23
    • 84863780073 scopus 로고    scopus 로고
    • Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm, Applied Mathematics and Computation
    • Ma WX, Zhu Z, (2012) Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm, Applied Mathematics and Computation. 218: 11871-11879.
    • (2012) , vol.218 , pp. 11871-11879
    • Ma, W.X.1    Zhu, Z.2
  • 24
    • 79551605767 scopus 로고    scopus 로고
    • Soliton solutions for a generalized fifth-order KdV equation with t-dependent coefficients
    • Triki H, Biswas A, (2011) Soliton solutions for a generalized fifth-order KdV equation with t-dependent coefficients. Waves in Random and Complex Media 21: 151-160.
    • (2011) Waves in Random and Complex Media , vol.21 , pp. 151-160
    • Triki, H.1    Biswas, A.2
  • 25
    • 80052684127 scopus 로고    scopus 로고
    • A new (2+1)-dimensional Korteweg-de-Vries equation and its extension to a new (3+1)-dimensional Kadomtsev-Petviashvili equation
    • doi:10.1088/0031-8949/84/03/035010
    • Wazwaz AM (2011) A new (2+1)-dimensional Korteweg-de-Vries equation and its extension to a new (3+1)-dimensional Kadomtsev-Petviashvili equation. Physica Scripta, doi:10.1088/0031-8949/84/03/035010.
    • (2011) Physica Scripta
    • Wazwaz, A.M.1
  • 27
    • 79960133842 scopus 로고    scopus 로고
    • A discrete model to study reaction-diffusion mechanics systems
    • doi: 10.1371/journal.pone.0021934
    • Weise LD, Nash MP, Panfilov AV, (2011) A discrete model to study reaction-diffusion mechanics systems. Plos One 6(7): e21934 doi:10.1371/journal.pone.0021934.
    • (2011) Plos One , vol.6 , Issue.7
    • Weise, L.D.1    Nash, M.P.2    Panfilov, A.V.3
  • 28
    • 79959591138 scopus 로고    scopus 로고
    • Travelling waves of delayed SIR epidemic model with nonlinear incidence rate and spatial diffusion
    • doi: 10.1371/journal.pone.0021128
    • Yang J, Liang S, Zhang Y, (2011) Travelling waves of delayed SIR epidemic model with nonlinear incidence rate and spatial diffusion. Plos One 6(6): e21128 doi:10.1371/journal.pone.0021128.
    • (2011) Plos One , vol.6 , Issue.6
    • Yang, J.1    Liang, S.2    Zhang, Y.3
  • 29
    • 37549033511 scopus 로고    scopus 로고
    • The (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
    • Wang M, Li X, Zhang J, (2008) The (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A 372: 417-423.
    • (2008) Physics Letters A , vol.372 , pp. 417-423
    • Wang, M.1    Li, X.2    Zhang, J.3
  • 30
    • 79551623747 scopus 로고    scopus 로고
    • Using (G′/G)-expansion method to seek traveling wave solution of Kolmogorov-Petrovskii-Piskunov equation
    • Feng J, Li W, Wan Q, (2011) Using (G′/G)-expansion method to seek traveling wave solution of Kolmogorov-Petrovskii-Piskunov equation. Applied Mathematics and Computation 217: 5860-5865.
    • (2011) Applied Mathematics and Computation , vol.217 , pp. 5860-5865
    • Feng, J.1    Li, W.2    Wan, Q.3
  • 31
    • 84855587077 scopus 로고    scopus 로고
    • The (G′/G)-expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equation
    • Article ID: 218216, doi:10.1155/2011/218216
    • Naher H, Abdullah FA, Akbar MA (2011) The (G′/G)-expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equation. Mathematical Problems in Engineering, Article ID: 218216, 11 pages, doi:10.1155/2011/218216.
    • (2011) Mathematical Problems in Engineering , pp. 11
    • Naher, H.1    Abdullah, F.A.2    Akbar, M.A.3
  • 32
    • 80052647793 scopus 로고    scopus 로고
    • Hyperbolic, trigonometric and rational function solutions of Hirota-Ramani equation via (G′/G)-expansion method
    • Article ID: 424801, 11 pages, doi:10.1155/2011/424801
    • Abazari R, Abazari R (2011) Hyperbolic, trigonometric and rational function solutions of Hirota-Ramani equation via (G′/G)-expansion method. Mathematical Problems in Engineering, Article ID: 424801, 11 pages, doi:10.1155/2011/424801.
    • (2011) Mathematical Problems in Engineering
    • Abazari, R.1    Abazari, R.2
  • 33
    • 77957835038 scopus 로고    scopus 로고
    • Applications of an Extended (G′/G)-Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics
    • Article ID 768573, 19 pages, doi:10.1155/2010/768573
    • Zayed EME, Al-Joudi S (2010) Applications of an Extended (G′/G)-Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics. Mathematical Problems in Engineering, Article ID 768573, 19 pages, doi:10.1155/2010/768573.
    • (2010) Mathematical Problems in Engineering
    • Zayed, E.M.E.1    Al-Joudi, S.2
  • 34
    • 77954654267 scopus 로고    scopus 로고
    • An improved (G′/G)-expansion method for solving nonlinear evolution equations
    • Zhang J, Jiang F, Zhao X, (2010) An improved (G′/G)-expansion method for solving nonlinear evolution equations. International Journal of Computer Mathematics 87: 1716-1725.
    • (2010) International Journal of Computer Mathematics , vol.87 , pp. 1716-1725
    • Zhang, J.1    Jiang, F.2    Zhao, X.3
  • 35
    • 80755169404 scopus 로고    scopus 로고
    • Application of the improved (G′/G)-expansion method for the Variant Boussinesq equations
    • Zhao YM, Yang YJ, Li W, (2011) Application of the improved (G′/G)-expansion method for the Variant Boussinesq equations. Applied Mathematical Sciences 5: 2855-2861.
    • (2011) Applied Mathematical Sciences , vol.5 , pp. 2855-2861
    • Zhao, Y.M.1    Yang, Y.J.2    Li, W.3
  • 38
    • 84866054269 scopus 로고    scopus 로고
    • Some new traveling wave solutions of the nonlinear reaction diffusion equation by using the improved (G′/G)-expansion method
    • Article ID: 871724, 17 pages, doi:10.1155/2012/871724
    • Naher H, Abdullah FA (2012) Some new traveling wave solutions of the nonlinear reaction diffusion equation by using the improved (G′/G)-expansion method. Mathematical Problems in Engineering, Article ID: 871724, 17 pages, doi:10.1155/2012/871724.
    • (2012) Mathematical Problems in Engineering
    • Naher, H.1    Abdullah, F.A.2
  • 39
    • 84859768511 scopus 로고    scopus 로고
    • A generalized and improved (G′/G)-expansion method for nonlinear evolution equations
    • Article ID: 459879, 22 pages, doi:10.1155/2012/459879
    • Akbar MA, Ali NHM, Zayed EME (2012) A generalized and improved (G′/G)-expansion method for nonlinear evolution equations. Mathematical Problems in Engineering Article ID: 459879, 22 pages, doi:10.1155/2012/459879.
    • (2012) Mathematical Problems in Engineering
    • Akbar, M.A.1    Ali, N.H.M.2    Zayed, E.M.E.3
  • 40
    • 79956122308 scopus 로고    scopus 로고
    • Traveling wave solutions for higher dimensional nonlinear evolution equations using the (G′/G)-expansion method
    • Zayed EME, (2010) Traveling wave solutions for higher dimensional nonlinear evolution equations using the (G′/G)-expansion method. Journal of Applied Mathematics & Informatics 28: 383-395.
    • (2010) Journal of Applied Mathematics & Informatics , vol.28 , pp. 383-395
    • Zayed, E.M.E.1
  • 41
    • 33645066098 scopus 로고    scopus 로고
    • An elliptic equation method and its applications in nonlinear evolution equations
    • Xu G, (2006) An elliptic equation method and its applications in nonlinear evolution equations. Chaos, Solitons and Fractals 29: 942-947.
    • (2006) Chaos, Solitons and Fractals , vol.29 , pp. 942-947
    • Xu, G.1
  • 42
    • 84858255171 scopus 로고    scopus 로고
    • New traveling wave solutions of the higher dimensional nonlinear evolution equation by the improved (G′/G)-expansion method
    • Naher H, Abdullah FA, Akbar MA, (2012) New traveling wave solutions of the higher dimensional nonlinear evolution equation by the improved (G′/G)-expansion method. World Applied Sciences Journal 16: 11-21.
    • (2012) World Applied Sciences Journal , vol.16 , pp. 11-21
    • Naher, H.1    Abdullah, F.A.2    Akbar, M.A.3


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