메뉴 건너뛰기




Volumn 14, Issue 5, 2009, Pages 1881-1890

Be careful with the Exp-function method

Author keywords

Exact solution; Exp function method; Nonlinear evolution equation; Simplest equation method

Indexed keywords

FUNCTIONS; NONLINEAR EQUATIONS;

EID: 56049095964     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2008.07.021     Document Type: Review
Times cited : (125)

References (52)
  • 1
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • He J.H., and Wu X.H. Exp-function method for nonlinear wave equations. Chaos Solitons Fract 30 (2006) 700-708
    • (2006) Chaos Solitons Fract , vol.30 , pp. 700-708
    • He, J.H.1    Wu, X.H.2
  • 2
    • 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 Fract 34 (2007) 1421-1429
    • (2007) Chaos Solitons Fract , vol.34 , pp. 1421-1429
    • He, J.H.1    Abdou, M.A.2
  • 3
    • 34748862326 scopus 로고    scopus 로고
    • Solitary solutions, periodic solutions and compaction-like solutions using the Exp-function method
    • Wu X.H., and He J.H. Solitary solutions, periodic solutions and compaction-like solutions using the Exp-function method. Comput Math Appl 54 (2007) 966-986
    • (2007) Comput Math Appl , vol.54 , pp. 966-986
    • Wu, X.H.1    He, J.H.2
  • 4
    • 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 (2007) 461-464
    • (2007) Int J Nonlinear Sci Numer Simul , vol.8 , pp. 461-464
    • Zhu, S.D.1
  • 5
    • 34548631824 scopus 로고    scopus 로고
    • New application of the Exp-function for improved Boussinesq equation
    • Abdou M.A., Soliman A.A., and El-Basyony S.T. New application of the Exp-function for improved Boussinesq equation. Phys Lett A 369 (2007) 469-475
    • (2007) Phys Lett A , vol.369 , pp. 469-475
    • Abdou, M.A.1    Soliman, A.A.2    El-Basyony, S.T.3
  • 6
    • 34548246435 scopus 로고    scopus 로고
    • Application of the Exp-function method for nonlinear evolution equations with variable coefficients
    • El-Wakil S.A., Madkour M.A., and Abdou M.A. Application of the Exp-function method for nonlinear evolution equations with variable coefficients. Phys Lett A 369 (2007) 62-69
    • (2007) Phys Lett A , vol.369 , pp. 62-69
    • El-Wakil, S.A.1    Madkour, M.A.2    Abdou, M.A.3
  • 7
    • 38149058867 scopus 로고    scopus 로고
    • New periodic wave solutions via Exp-function method
    • El-Wakil S.A., Abdou M.A., and Hendi A. New periodic wave solutions via Exp-function method. Phys Lett A 372 (2008) 830-840
    • (2008) Phys Lett A , vol.372 , pp. 830-840
    • El-Wakil, S.A.1    Abdou, M.A.2    Hendi, A.3
  • 8
    • 35348977120 scopus 로고    scopus 로고
    • Exp-function method for solving Maccari's system
    • Zhang S. Exp-function method for solving Maccari's system. Phys Lett A 371 (2007) 65-71
    • (2007) Phys Lett A , vol.371 , pp. 65-71
    • Zhang, S.1
  • 9
    • 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 (2007) 213-219
    • (2007) Phys Lett A , vol.365 , pp. 213-219
    • Ebaid, A.1
  • 10
    • 37549053290 scopus 로고    scopus 로고
    • New solitary solutions for the MBBM equations using Exp-function method
    • Yusufoǧlu E. New solitary solutions for the MBBM equations using Exp-function method. Phys Lett A 372 (2008) 442-446
    • (2008) Phys Lett A , vol.372 , pp. 442-446
    • Yusufoǧlu, E.1
  • 11
    • 42749088097 scopus 로고    scopus 로고
    • A novel approach for solving the Fisher using Exp-function method
    • Ozis T., and Koroglu C. A novel approach for solving the Fisher using Exp-function method. Phys Lett A 372 (2008) 3836-3840
    • (2008) Phys Lett A , vol.372 , pp. 3836-3840
    • Ozis, T.1    Koroglu, C.2
  • 12
    • 40949138221 scopus 로고    scopus 로고
    • Soliton and periodic solutions for the fifth-order KdV equation with the Exp-function method
    • Chun C. Soliton and periodic solutions for the fifth-order KdV equation with the Exp-function method. Phys Lett A 372 (2008) 2760-2766
    • (2008) Phys Lett A , vol.372 , pp. 2760-2766
    • Chun, C.1
  • 13
    • 85196183046 scopus 로고    scopus 로고
    • Soliman AA. Chaos, solitons and fractals, exact solutions of the KdV-Burgers equation by Exp-function method. Chaos Solitons Fract, doi:10.1016/J.chaos.2008.04.038.
    • Soliman AA. Chaos, solitons and fractals, exact solutions of the KdV-Burgers equation by Exp-function method. Chaos Solitons Fract, doi:10.1016/J.chaos.2008.04.038.
  • 14
    • 42749096687 scopus 로고    scopus 로고
    • Application of the Exp-function method to Riccati equation and new exact solutions with three arbitrary functions of Broer-Kaup-Kupershmidt equations
    • Zhang S. Application of the Exp-function method to Riccati equation and new exact solutions with three arbitrary functions of Broer-Kaup-Kupershmidt equations. Phys Lett A 372 (2008) 1873-1880
    • (2008) Phys Lett A , vol.372 , pp. 1873-1880
    • Zhang, S.1
  • 15
    • 38949119784 scopus 로고    scopus 로고
    • Exact solutions for nonlinear evolution equation using Exp-function method
    • Bekir A., and Boz A. Exact solutions for nonlinear evolution equation using Exp-function method. Phys Lett A 372 (2008) 1619-1625
    • (2008) Phys Lett A , vol.372 , pp. 1619-1625
    • Bekir, A.1    Boz, A.2
  • 16
    • 0010251877 scopus 로고
    • Exact soliton solutions of the generalized evolution equation of wave dynamics
    • Kudryashov N.A. Exact soliton solutions of the generalized evolution equation of wave dynamics. J Appl Math Mech 52 3 (1988) 361-365
    • (1988) J Appl Math Mech , vol.52 , Issue.3 , pp. 361-365
    • Kudryashov, N.A.1
  • 17
    • 36749112076 scopus 로고
    • The Painleve property for partial differential equations
    • Weiss J., Tabor M., and Carnevalle G. The Painleve property for partial differential equations. J Math Phys 24 (1983) 522-526
    • (1983) J Math Phys , vol.24 , pp. 522-526
    • Weiss, J.1    Tabor, M.2    Carnevalle, G.3
  • 18
    • 36749110322 scopus 로고
    • The Painleve property for partial differential equations. II: Backlund transformation, Lax pairs, and the Schwarzian derivative
    • Weiss J. The Painleve property for partial differential equations. II: Backlund transformation, Lax pairs, and the Schwarzian derivative. J Math Phys 24 (1983) 1405-1413
    • (1983) J Math Phys , vol.24 , pp. 1405-1413
    • Weiss, J.1
  • 19
    • 85196153418 scopus 로고    scopus 로고
    • Kudryashov NA. Analytical theory of nonlinear differential equations. Moskow-Igevsk: Institute of Computer Investigations; 2004. p. 360 [in Russian].
    • Kudryashov NA. Analytical theory of nonlinear differential equations. Moskow-Igevsk: Institute of Computer Investigations; 2004. p. 360 [in Russian].
  • 21
    • 36149032371 scopus 로고
    • Exact solitary waves in a convecting fluid
    • Lou S.Y., Huang G.X., and Ruan H.Y. Exact solitary waves in a convecting fluid. J Phys A: Math Gen 24 11 (1991) L587-L590
    • (1991) J Phys A: Math Gen , vol.24 , Issue.11
    • Lou, S.Y.1    Huang, G.X.2    Ruan, H.Y.3
  • 22
    • 0030284901 scopus 로고    scopus 로고
    • An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations
    • Parkes E.J., and Duffy B.R. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput Phys Commun 98 (1996) 288-300
    • (1996) Comput Phys Commun , vol.98 , pp. 288-300
    • Parkes, E.J.1    Duffy, B.R.2
  • 23
    • 0004483962 scopus 로고    scopus 로고
    • The tanh method. I: Exact solutions of nonlinear evolution and wave equations
    • Malfliet W., and Hereman W.W. The tanh method. I: Exact solutions of nonlinear evolution and wave equations. Phys Scripta 54 (1996) 563-568
    • (1996) Phys Scripta , vol.54 , pp. 563-568
    • Malfliet, W.1    Hereman, W.W.2
  • 24
    • 0000607676 scopus 로고
    • Exact solutions of the generalized Kuramoto-Sivashinsky equation
    • Kudryashov N.A. Exact solutions of the generalized Kuramoto-Sivashinsky equation. Phys Lett A 147 (1990) 287-291
    • (1990) Phys Lett A , vol.147 , pp. 287-291
    • Kudryashov, N.A.1
  • 25
    • 13444309466 scopus 로고    scopus 로고
    • Simplest equation method to look for exact solutions of nonlinear differential equations
    • Kudryashov N.A. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fract 24 (2005) 1217-1231
    • (2005) Chaos Solitons Fract , vol.24 , pp. 1217-1231
    • Kudryashov, N.A.1
  • 26
    • 20444493250 scopus 로고    scopus 로고
    • Exact solitary waves of the Fisher equations
    • Kudryashov N.A. Exact solitary waves of the Fisher equations. Phys Lett A 342 (2005) 99-106
    • (2005) Phys Lett A , vol.342 , pp. 99-106
    • Kudryashov, N.A.1
  • 27
    • 0001635608 scopus 로고
    • On types nonlinear nonintegrable differential equations with exact solutions
    • Kudryashov N.A. On types nonlinear nonintegrable differential equations with exact solutions. Phys Lett A 155 (1991) 269-275
    • (1991) Phys Lett A , vol.155 , pp. 269-275
    • Kudryashov, N.A.1
  • 28
    • 0030597464 scopus 로고    scopus 로고
    • Solitary waves in active-dissipative dispersive media
    • Kudryashov N.A., and Zargaryan E.D. Solitary waves in active-dissipative dispersive media. J Phys A: Math Gen 29 (1996) 8067-8077
    • (1996) J Phys A: Math Gen , vol.29 , pp. 8067-8077
    • Kudryashov, N.A.1    Zargaryan, E.D.2
  • 29
    • 38249009217 scopus 로고
    • Partial differential equations with solutions having movable first-order singularities
    • Kudryashov N.A. Partial differential equations with solutions having movable first-order singularities. Phys Lett A 169 (1992) 237-242
    • (1992) Phys Lett A , vol.169 , pp. 237-242
    • Kudryashov, N.A.1
  • 30
    • 34250077953 scopus 로고
    • Multi-phase and rational solutions of one family of nonlinear equations
    • Kudryashov N.A. Multi-phase and rational solutions of one family of nonlinear equations. Theor Math Phys 94 3 (1993) 393-407
    • (1993) Theor Math Phys , vol.94 , Issue.3 , pp. 393-407
    • Kudryashov, N.A.1
  • 31
    • 8744316856 scopus 로고    scopus 로고
    • Exact solutions of the Burgers-Huxley equation
    • Yefimova O.Yu., and Kudryashov N.A. Exact solutions of the Burgers-Huxley equation. J Appl Math Mech 68 3 (2004) 413-420
    • (2004) J Appl Math Mech , vol.68 , Issue.3 , pp. 413-420
    • Yefimova, O.Yu.1    Kudryashov, N.A.2
  • 32
    • 0000092898 scopus 로고
    • Painleve analysis and Backlund transformations in the Kuramoto-Sivashinsky equation
    • Conte R., and Musette M. Painleve analysis and Backlund transformations in the Kuramoto-Sivashinsky equation. J Phys A: Math Gen 22 (1989) 169-177
    • (1989) J Phys A: Math Gen , vol.22 , pp. 169-177
    • Conte, R.1    Musette, M.2
  • 33
    • 0003774151 scopus 로고    scopus 로고
    • The Painleve property, one century later
    • Springer-Verlag, New York p. 77-180
    • Conte R. The Painleve property, one century later. CRM series in mathematical physics (1999), Springer-Verlag, New York p. 77-180
    • (1999) CRM series in mathematical physics
    • Conte, R.1
  • 34
    • 33344476528 scopus 로고    scopus 로고
    • The singular manifold method and exact periodic wave solutions to a restricted BLP dispersive long wave system
    • Peng Y.Z., and Krishnan E.V. The singular manifold method and exact periodic wave solutions to a restricted BLP dispersive long wave system. Rep Math Phys 56 (2005) 367-378
    • (2005) Rep Math Phys , vol.56 , pp. 367-378
    • Peng, Y.Z.1    Krishnan, E.V.2
  • 37
    • 0016369301 scopus 로고
    • The inverse scattering transform-fourier analysis for nonlinear problems
    • Ablowitz M.J., Kaup D.J., Newell A.C., and Segur H. The inverse scattering transform-fourier analysis for nonlinear problems. Stud Appl Math 53 (1974) 249-315
    • (1974) Stud Appl Math , vol.53 , pp. 249-315
    • Ablowitz, M.J.1    Kaup, D.J.2    Newell, A.C.3    Segur, H.4
  • 38
    • 35949040541 scopus 로고
    • Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons
    • Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys Rev Lett 27 (1971) 1192-1194
    • (1971) Phys Rev Lett , vol.27 , pp. 1192-1194
    • Hirota, R.1
  • 40
    • 0000332692 scopus 로고
    • On a quasilinear parabolic equation occurring in aerodynamics
    • Cole J.D. On a quasilinear parabolic equation occurring in aerodynamics. Quart Appl Math 9 (1951) 225-236
    • (1951) Quart Appl Math , vol.9 , pp. 225-236
    • Cole, J.D.1
  • 41
    • 0035813363 scopus 로고    scopus 로고
    • New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations
    • Fu Z.T., Liu S.K., Liu S.D., et al. New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Phys Lett A 290 1-2 (2001) 72-76
    • (2001) Phys Lett A , vol.290 , Issue.1-2 , pp. 72-76
    • Fu, Z.T.1    Liu, S.K.2    Liu, S.D.3
  • 42
    • 0035828886 scopus 로고    scopus 로고
    • Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
    • Liu S.K., Fu Z.T., Liu S.D., et al. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys Lett A 289 1-2 (2001) 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
  • 43
    • 41649083940 scopus 로고    scopus 로고
    • An effective method for finding special solutions of nonlinear differential equations with variable coefficients
    • Qin M., and Fan G. An effective method for finding special solutions of nonlinear differential equations with variable coefficients. Phys Lett A 372 (2008) 3240-3242
    • (2008) Phys Lett A , vol.372 , pp. 3240-3242
    • Qin, M.1    Fan, G.2
  • 44
    • 42649120956 scopus 로고    scopus 로고
    • Exact travelling wave solutions for the Zakharov-Kuznetsov equation
    • Peng Z.Y. Exact travelling wave solutions for the Zakharov-Kuznetsov equation. Appl Math Comput 199 (2008) 397-405
    • (2008) Appl Math Comput , vol.199 , pp. 397-405
    • Peng, Z.Y.1
  • 45
    • 0348201928 scopus 로고    scopus 로고
    • Exact solutions of the fifth-order equation for describing waves on the water
    • Kudryashov N.A., and Sukharev M.B. Exact solutions of the fifth-order equation for describing waves on the water. J Appl Math Mech 65 5 (2001) 855-865
    • (2001) J Appl Math Mech , vol.65 , Issue.5 , pp. 855-865
    • Kudryashov, N.A.1    Sukharev, M.B.2
  • 46
    • 18544377979 scopus 로고    scopus 로고
    • Fuchs indices and the first integrals of nonlinear differential equations
    • Kudryashov N.A. Fuchs indices and the first integrals of nonlinear differential equations. Chaos Solitons Fract 26 2 (2005) 591-603
    • (2005) Chaos Solitons Fract , vol.26 , Issue.2 , pp. 591-603
    • Kudryashov, N.A.1
  • 47
    • 33947182950 scopus 로고    scopus 로고
    • Polygons of differential equations for finding exact solutions
    • Kudryashov N.A., and Demina M.V. Polygons of differential equations for finding exact solutions. Chaos Solitons Fract 33 (2007) 1480-1496
    • (2007) Chaos Solitons Fract , vol.33 , pp. 1480-1496
    • Kudryashov, N.A.1    Demina, M.V.2
  • 48
    • 45349108626 scopus 로고    scopus 로고
    • Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation
    • Kudryashov N.A. Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation. Regul Chaotic Dynam 13 3 (2008) 234-238
    • (2008) Regul Chaotic Dynam , vol.13 , Issue.3 , pp. 234-238
    • Kudryashov, N.A.1
  • 49
    • 45849149292 scopus 로고    scopus 로고
    • Traveling wave solutions for some time-delayed equations through factorizations
    • Fahmy E.S. Traveling wave solutions for some time-delayed equations through factorizations. Chaos Solitons Fract 38 (2008) 1209-1216
    • (2008) Chaos Solitons Fract , vol.38 , pp. 1209-1216
    • Fahmy, E.S.1
  • 50
    • 36249009075 scopus 로고    scopus 로고
    • New periodic waves solutions for the shallow water of the generalized Klein-Gordon equation
    • Elgarayhi A. New periodic waves solutions for the shallow water of the generalized Klein-Gordon equation. Commun Nonlinear Sci Numer Simul 13 (2008) 877-888
    • (2008) Commun Nonlinear Sci Numer Simul , vol.13 , pp. 877-888
    • Elgarayhi, A.1
  • 51
    • 33749515412 scopus 로고    scopus 로고
    • A unified trial function method in finding the explicit and exact solutions to three NPDs
    • Xie Y., and Tang J.S. A unified trial function method in finding the explicit and exact solutions to three NPDs. Phys Scripta 74 2 (2006) 197-200
    • (2006) Phys Scripta , vol.74 , Issue.2 , pp. 197-200
    • Xie, Y.1    Tang, J.S.2
  • 52
    • 33745644740 scopus 로고    scopus 로고
    • A unified method for solving sinh-Gordon type equations, Nuovo Cimento
    • Xie Y., and Tang J.S. A unified method for solving sinh-Gordon type equations, Nuovo Cimento. Pisica B 121 2 (2006) 115-120
    • (2006) Pisica B , vol.121 , Issue.2 , pp. 115-120
    • Xie, Y.1    Tang, J.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.