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Volumn 56, Issue 5, 2008, Pages 1451-1456

Application of Exp-function method for (3 + 1)-dimensional nonlinear evolution equations

Author keywords

Exact solutions; Exp function method; Kadomstev Petviashvili equation; Potantial YTSF equation; Solitons

Indexed keywords

BESSEL FUNCTIONS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); FUNCTION EVALUATION; FUNCTIONS; MATHEMATICAL MORPHOLOGY; MICROFLUIDICS; NONLINEAR PROGRAMMING; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; WAVE EQUATIONS; WAVES;

EID: 46449139466     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2008.02.045     Document Type: Article
Times cited : (47)

References (41)
  • 2
    • 0001229736 scopus 로고
    • Solitary wave solutions of nonlinear wave equations
    • Malfliet W. Solitary wave solutions of nonlinear wave equations. Amer. J. Phys. 60 (1992) 650-654
    • (1992) Amer. J. Phys. , vol.60 , pp. 650-654
    • Malfliet, W.1
  • 3
    • 0004483962 scopus 로고    scopus 로고
    • The tanh method. I: Exact solutions of nonlinear evolution and wave equations
    • Malfliet W., and Hereman W. The tanh method. I: Exact solutions of nonlinear evolution and wave equations. Phys. Scr. 54 (1996) 563-568
    • (1996) Phys. Scr. , vol.54 , pp. 563-568
    • Malfliet, W.1    Hereman, W.2
  • 4
    • 3042750187 scopus 로고    scopus 로고
    • The tanh method for travelling wave solutions of nonlinear equations
    • Wazwaz A.M. The tanh method for travelling wave solutions of nonlinear equations. Appl. Math. Comput. 154 3 (2004) 713-723
    • (2004) Appl. Math. Comput. , vol.154 , Issue.3 , pp. 713-723
    • Wazwaz, A.M.1
  • 5
    • 33747348716 scopus 로고    scopus 로고
    • New exact travelling wave solutions using modified extended tanh-function method
    • El-Wakil S.A., and Abdou M.A. New exact travelling wave solutions using modified extended tanh-function method. Chaos Solitons Fractals 31 4 (2007) 840-852
    • (2007) Chaos Solitons Fractals , vol.31 , Issue.4 , pp. 840-852
    • El-Wakil, S.A.1    Abdou, M.A.2
  • 6
    • 0034606149 scopus 로고    scopus 로고
    • Extended tanh-function method and its applications to nonlinear equations
    • Fan E. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277 (2000) 212
    • (2000) Phys. Lett. A , vol.277 , pp. 212
    • Fan, E.1
  • 7
    • 34247279667 scopus 로고    scopus 로고
    • The extended tanh method for abundant solitary wave solutions of nonlinear wave equations
    • Wazwaz A.M. The extended tanh method for abundant solitary wave solutions of nonlinear wave equations. Appl. Math. Comput. 187 2 (2007) 1131-1142
    • (2007) Appl. Math. Comput. , vol.187 , Issue.2 , pp. 1131-1142
    • Wazwaz, A.M.1
  • 8
    • 28844476111 scopus 로고    scopus 로고
    • Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method
    • Wazwaz A.M. Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method. Comput. Math. Appl. 50 10-11 (2005) 1685-1696
    • (2005) Comput. Math. Appl. , vol.50 , Issue.10-11 , pp. 1685-1696
    • Wazwaz, A.M.1
  • 9
    • 12944300203 scopus 로고    scopus 로고
    • A sine-cosine method for handling nonlinear wave equations
    • Wazwaz A.M. A sine-cosine method for handling nonlinear wave equations. Math. Comput. Model. 40 (2004) 499-508
    • (2004) Math. Comput. Model. , vol.40 , pp. 499-508
    • Wazwaz, A.M.1
  • 10
    • 0043093642 scopus 로고    scopus 로고
    • A simple transformation for nonlinear waves
    • Yan C. A simple transformation for nonlinear waves. Phys. Lett. A 224 (1996) 77
    • (1996) Phys. Lett. A , vol.224 , pp. 77
    • Yan, C.1
  • 11
    • 4344673183 scopus 로고    scopus 로고
    • A note on the homogeneous balance method
    • Fan E., and Zhang H. A note on the homogeneous balance method. Phys. Lett. A 246 (1998) 403-406
    • (1998) Phys. Lett. A , vol.246 , pp. 403-406
    • Fan, E.1    Zhang, H.2
  • 12
    • 0001051423 scopus 로고    scopus 로고
    • Exact solutions for a compound KdV-Burgers equation
    • Wang M.L. Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213 (1996) 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 differential-difference equations
    • Dai C.Q., and Zhang J.F. Jacobian elliptic function method for nonlinear differential-difference equations. Chaos Solitons Fractals 27 (2006) 1042-1049
    • (2006) Chaos Solitons Fractals , vol.27 , pp. 1042-1049
    • Dai, C.Q.1    Zhang, J.F.2
  • 14
    • 0037121825 scopus 로고    scopus 로고
    • Applications of the Jacobi elliptic function method to special-type nonlinear equations
    • Fan E., and Zhang J. Applications of the Jacobi elliptic function method to special-type nonlinear equations. Phys. Lett. A 305 (2002) 383-392
    • (2002) Phys. Lett. A , vol.305 , pp. 383-392
    • Fan, E.1    Zhang, J.2
  • 15
    • 0035828886 scopus 로고    scopus 로고
    • Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
    • Liu S., Fu Z., Liu S., and Zhao Q. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys. Lett. A 289 (2001) 69
    • (2001) Phys. Lett. A , vol.289 , pp. 69
    • Liu, S.1    Fu, Z.2    Liu, S.3    Zhao, Q.4
  • 16
    • 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., Zhi H.Y., and Zhang H.Q. Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system. Chaos Solitons Fractals 28 (2006) 112-126
    • (2006) Chaos Solitons Fractals , vol.28 , pp. 112-126
    • Zhao, X.Q.1    Zhi, H.Y.2    Zhang, H.Q.3
  • 17
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • He J.H. Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30 (2006) 700-708
    • (2006) Chaos Solitons Fractals , vol.30 , pp. 700-708
    • He, J.H.1
  • 18
    • 34250163508 scopus 로고    scopus 로고
    • New periodic solutions for nonlinear evolution equations using Exp-function method
    • He J.H., and Abdou M.A. New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos Solitons Fractals 34 5 (2007) 1421-1429
    • (2007) Chaos Solitons Fractals , vol.34 , Issue.5 , pp. 1421-1429
    • He, J.H.1    Abdou, M.A.2
  • 19
    • 33745810605 scopus 로고    scopus 로고
    • The extended F-expansion method and its application for a class of nonlinear evolution equations
    • Abdou M.A. The extended F-expansion method and its application for a class of nonlinear evolution equations. Chaos Solitons Fractals 31 (2007) 95-104
    • (2007) Chaos Solitons Fractals , vol.31 , pp. 95-104
    • Abdou, M.A.1
  • 20
    • 24344445510 scopus 로고    scopus 로고
    • A generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation
    • Ren Y.J., and Zhang H.Q. A generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation. Chaos Solitons Fractals 27 (2006) 959-979
    • (2006) Chaos Solitons Fractals , vol.27 , pp. 959-979
    • Ren, Y.J.1    Zhang, H.Q.2
  • 21
    • 30644460638 scopus 로고    scopus 로고
    • The improved F-expansion method and its applications
    • Zhang J.L., Wang M.L., Wang Y.M., and Fang Z.D. The improved F-expansion method and its applications. Phys. Lett. A 350 (2006) 103
    • (2006) Phys. Lett. A , vol.350 , pp. 103
    • Zhang, J.L.1    Wang, M.L.2    Wang, Y.M.3    Fang, Z.D.4
  • 22
    • 33748919061 scopus 로고    scopus 로고
    • Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations
    • Ganji D.D., and Sadighi A. Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations. Int. J. Nonlinear Sci. Numer. Simul. 7 4 (2006) 411-418
    • (2006) Int. J. Nonlinear Sci. Numer. Simul. , vol.7 , Issue.4 , pp. 411-418
    • Ganji, D.D.1    Sadighi, A.2
  • 23
    • 34249884542 scopus 로고    scopus 로고
    • Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method
    • Ozis T., and Yildirim A. Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method. Int. J. Nonlinear Sci. Numer. Simul. 8 2 (2007) 239-242
    • (2007) Int. J. Nonlinear Sci. Numer. Simul. , vol.8 , Issue.2 , pp. 239-242
    • Ozis, T.1    Yildirim, A.2
  • 24
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He J.H. Some asymptotic methods for strongly nonlinear equations. Internat. J. Modern Phys. B 20 10 (2006) 1141-1199
    • (2006) Internat. J. Modern Phys. B , vol.20 , Issue.10 , pp. 1141-1199
    • He, J.H.1
  • 25
    • 30344475545 scopus 로고    scopus 로고
    • Construction of solitary solution and compacton-like solution by variational iteration method
    • He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos Solitons Fractals 29 1 (2006) 108-113
    • (2006) Chaos Solitons Fractals , vol.29 , Issue.1 , pp. 108-113
    • He, J.H.1    Wu, X.H.2
  • 26
    • 46449115128 scopus 로고    scopus 로고
    • J.H. He, Non-Perturbative Methods for Strongly Nonlinear Problems, Dissertation. de-Verlag im Internet GmbH, Berlin, Germany, 2006
    • J.H. He, Non-Perturbative Methods for Strongly Nonlinear Problems, Dissertation. de-Verlag im Internet GmbH, Berlin, Germany, 2006
  • 27
    • 9644255681 scopus 로고    scopus 로고
    • Symbolic computation in non-linear evolution equation: application to (3+1)-dimensional Kadomtsev-Petviashvili equation
    • Xie F.D., Zhang Y., and Lu Z.S. Symbolic computation in non-linear evolution equation: application to (3+1)-dimensional Kadomtsev-Petviashvili equation. Chaos Solitons Fractals 24 (2005) 257-263
    • (2005) Chaos Solitons Fractals , vol.24 , pp. 257-263
    • Xie, F.D.1    Zhang, Y.2    Lu, Z.S.3
  • 28
    • 33646146933 scopus 로고    scopus 로고
    • New doubly periodic and multiple soliton solutions of the generalized (3+1)-dimensional Kadomtsev-Petviashvilli equation with variable coefficients
    • Zhao H., and Bai C. New doubly periodic and multiple soliton solutions of the generalized (3+1)-dimensional Kadomtsev-Petviashvilli equation with variable coefficients. Chaos Solitons Fractals 30 (2006) 217-226
    • (2006) Chaos Solitons Fractals , vol.30 , pp. 217-226
    • Zhao, H.1    Bai, C.2
  • 29
    • 2042523036 scopus 로고    scopus 로고
    • New explicit solitary wave solutions for (2+1)-dimensional Boussinesq equation and (3+1)-dimensional KP equation
    • Chen Y., Yan Z., and Zhang H. New explicit solitary wave solutions for (2+1)-dimensional Boussinesq equation and (3+1)-dimensional KP equation. Phys. Lett. A 307 (2003) 107-113
    • (2003) Phys. Lett. A , vol.307 , pp. 107-113
    • Chen, Y.1    Yan, Z.2    Zhang, H.3
  • 30
    • 34248403766 scopus 로고    scopus 로고
    • A new variable coefficient Korteweg-de Vries equation-based sub-equation method and its application to the (3+1)-dimensional potential-YTSF equation
    • Song L., and Zhang H. A new variable coefficient Korteweg-de Vries equation-based sub-equation method and its application to the (3+1)-dimensional potential-YTSF equation. Appl. Math. Comput. 189 (2007) 560-566
    • (2007) Appl. Math. Comput. , vol.189 , pp. 560-566
    • Song, L.1    Zhang, H.2
  • 31
    • 34247093769 scopus 로고    scopus 로고
    • Non-travelling wave solutions to a (3+1)-dimensional potential-YTSF equation and a simplified model for reacting mixtures
    • Zhang T., Xuan H.-N., Zhang D.-F., and Wang C.-J. Non-travelling wave solutions to a (3+1)-dimensional potential-YTSF equation and a simplified model for reacting mixtures. Chaos Solitons Fractals 34 (2007) 1006-1013
    • (2007) Chaos Solitons Fractals , vol.34 , pp. 1006-1013
    • Zhang, T.1    Xuan, H.-N.2    Zhang, D.-F.3    Wang, C.-J.4
  • 32
    • 34748862326 scopus 로고    scopus 로고
    • Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method
    • Wu X.H., and He J.H. Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method. Comput. Math. Appl. 54 7-8 (2007) 966-986
    • (2007) Comput. Math. Appl. , vol.54 , Issue.7-8 , pp. 966-986
    • Wu, X.H.1    He, J.H.2
  • 33
    • 34247350849 scopus 로고    scopus 로고
    • Application of Exp-function method to a KdV equation with variable coefficients
    • Zhang S. Application of Exp-function method to a KdV equation with variable coefficients. Phys. Lett. A 365 5-6 (2007) 448-453
    • (2007) Phys. Lett. A , vol.365 , Issue.5-6 , pp. 448-453
    • Zhang, S.1
  • 34
    • 46449105952 scopus 로고    scopus 로고
    • S. Zhang, Application of Exp-function method to high-dimensional nonlinear evolution equations, Chaos, Solitons and Fractals (in press)
    • S. Zhang, Application of Exp-function method to high-dimensional nonlinear evolution equations, Chaos, Solitons and Fractals (in press)
  • 35
    • 34147152832 scopus 로고    scopus 로고
    • Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method
    • Ebaid A. Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method. Phys. Lett. A 365 3 (2007) 213-219
    • (2007) Phys. Lett. A , vol.365 , Issue.3 , pp. 213-219
    • Ebaid, A.1
  • 36
    • 34548246435 scopus 로고    scopus 로고
    • Application of Exp-function method for nonlinear evolution equations with variable coefficients
    • El-Wakil S.A., Madkour M.A., and Abdou M.A. Application of Exp-function method for nonlinear evolution equations with variable coefficients. Phys. Lett. A 369 1-2 (2007) 62-69
    • (2007) Phys. Lett. A , vol.369 , Issue.1-2 , pp. 62-69
    • El-Wakil, S.A.1    Madkour, M.A.2    Abdou, M.A.3
  • 37
    • 34548577315 scopus 로고    scopus 로고
    • Exp-function method for the hybrid-lattice system
    • Zhu S.D. Exp-function method for the hybrid-lattice system. Int. J. Nonlinear Sci. Numer. Simul. 8 3 (2007) 461-464
    • (2007) Int. J. Nonlinear Sci. Numer. Simul. , vol.8 , Issue.3 , pp. 461-464
    • Zhu, S.D.1
  • 38
    • 34548577316 scopus 로고    scopus 로고
    • Exp-function method for the discrete mKdV lattice
    • Zhu S.D. Exp-function method for the discrete mKdV lattice. Int. J. Nonlinear Sci. Numer. Simul. 8 3 (2007) 465-468
    • (2007) Int. J. Nonlinear Sci. Numer. Simul. , vol.8 , Issue.3 , pp. 465-468
    • Zhu, S.D.1
  • 39
    • 36248983300 scopus 로고    scopus 로고
    • Exact solutions for a class of nonlinear partial differential equations using Exp-function method
    • Bekir A., and Boz A. Exact solutions for a class of nonlinear partial differential equations using Exp-function method. Int. J. Nonlinear Sci. Numer. Simul. 8 5 (2007) 505-512
    • (2007) Int. J. Nonlinear Sci. Numer. Simul. , vol.8 , Issue.5 , pp. 505-512
    • Bekir, A.1    Boz, A.2
  • 40
    • 34548631824 scopus 로고    scopus 로고
    • New application of Exp-function method for improved Boussinesq equation
    • Abdou M.A. New application of Exp-function method for improved Boussinesq equation. Phys. Lett. A 369 (2007) 469-475
    • (2007) Phys. Lett. A , vol.369 , pp. 469-475
    • Abdou, M.A.1
  • 41
    • 0242318417 scopus 로고    scopus 로고
    • New families of nontravelling wave solutions to a new (3+1)-dimensional potential-YTSF equation
    • Yan Z. New families of nontravelling wave solutions to a new (3+1)-dimensional potential-YTSF equation. Phys. Lett. A 318 (2003) 78-83
    • (2003) Phys. Lett. A , vol.318 , pp. 78-83
    • Yan, Z.1


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