메뉴 건너뛰기




Volumn 14, Issue 9-10, 2009, Pages 3507-3529

Seven common errors in finding exact solutions of nonlinear differential equations

Author keywords

Common error; Exact solution; Exp function method; Nonlinear evolution equation; Tanh function method; Truncated expansion method

Indexed keywords

NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; SOLITONS;

EID: 63449123795     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.01.023     Document Type: Review
Times cited : (233)

References (76)
  • 1
    • 33846361348 scopus 로고
    • Interaction of solitons in a collisionless plasma and the recurrence of initial states
    • Zabusky N.J., and Kruskal M.D. Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys Rev Lett 15 (1965) 240-243
    • (1965) Phys Rev Lett , vol.15 , pp. 240-243
    • Zabusky, N.J.1    Kruskal, M.D.2
  • 3
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • Lax P.D. Integrals of nonlinear equations of evolution and solitary waves. Commun Pure Appl Math 21 (1968) 467-490
    • (1968) Commun Pure Appl Math , vol.21 , pp. 467-490
    • Lax, P.D.1
  • 4
    • 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
  • 6
    • 35949040541 scopus 로고
    • Exact solution of the Korteweg-de Vries for multiple collisions of solutions
    • Hirota R. Exact solution of the Korteweg-de Vries for multiple collisions of solutions. Phys Rev Lett 27 (1971) 1192-1194
    • (1971) Phys Rev Lett , vol.27 , pp. 1192-1194
    • Hirota, R.1
  • 7
    • 4344659813 scopus 로고    scopus 로고
    • Analitical theory of nonlinear differential equations
    • Institute of Computer Investigations;, in Russian
    • Kudryashov NA. Analitical theory of nonlinear differential equations. Moskow-Igevsk. Institute of Computer Investigations; 2004 [in Russian].
    • (2004) Moskow-Igevsk
    • Kudryashov, N.A.1
  • 8
    • 85196190996 scopus 로고    scopus 로고
    • Methods of nonlinear equations of mathematical physics and mechanics
    • Polyanin A.D., Zaitsev V.F., and Zhyrov A.I. Methods of nonlinear equations of mathematical physics and mechanics. Moscow Fizmatlit (2005)
    • (2005) Moscow Fizmatlit
    • Polyanin, A.D.1    Zaitsev, V.F.2    Zhyrov, A.I.3
  • 9
    • 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
  • 10
    • 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
  • 12
    • 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) 360-365
    • (1988) J Appl Math Mech , vol.52 , Issue.3 , pp. 360-365
    • Kudryashov, N.A.1
  • 13
    • 0000092898 scopus 로고
    • Painlevé analysis and Backlund transformations in the Kuramoto-Sivashinsky equation
    • Conte R., and Musette M. Painlevé 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
  • 14
    • 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
  • 15
    • 30244439261 scopus 로고
    • Exact soliton solutions of nonlinear wave equations arising in mechanics
    • Kudryashov N.A. Exact soliton solutions of nonlinear wave equations arising in mechanics. J Appl Math Mech 54 3 (1990) 450-453
    • (1990) J Appl Math Mech , vol.54 , Issue.3 , pp. 450-453
    • Kudryashov, N.A.1
  • 16
    • 0001635608 scopus 로고
    • On types of nonlinear nonintegrable equations with exact solutions
    • Kudryashov N.A. On types of nonlinear nonintegrable equations with exact solutions. Phys Lett A 155 (1991) 269-275
    • (1991) Phys Lett A , vol.155 , pp. 269-275
    • Kudryashov, N.A.1
  • 17
    • 38249009217 scopus 로고
    • Partial differential equations with solutions having movable first-order ingularities
    • Kudryashov N.A. Partial differential equations with solutions having movable first-order ingularities. Phys Lett A 169 (1992) 237-242
    • (1992) Phys Lett A , vol.169 , pp. 237-242
    • Kudryashov, N.A.1
  • 18
    • 0039538443 scopus 로고
    • Truncated expansions and nonlinear integrable partial differential equations
    • Kudryashov N.A. Truncated expansions and nonlinear integrable partial differential equations. Phys Lett A 178 (1993) 99-104
    • (1993) Phys Lett A , vol.178 , pp. 99-104
    • Kudryashov, N.A.1
  • 19
    • 21344478240 scopus 로고
    • From singular manifold equations to integrable evolution equations
    • Kudryashov N.A. From singular manifold equations to integrable evolution equations. J Phys A Math Gen 27 (1994) 2457-2470
    • (1994) J Phys A Math Gen , vol.27 , pp. 2457-2470
    • Kudryashov, N.A.1
  • 20
    • 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
  • 21
    • 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
  • 22
    • 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 Soliton Fract 24 (2005) 1217-1231
    • (2005) Chaos Soliton Fract , vol.24 , pp. 1217-1231
    • Kudryashov, N.A.1
  • 23
    • 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
  • 24
    • 33947182950 scopus 로고    scopus 로고
    • Polygons of differential equation for finding exact solutions
    • Kudryashov N.A., and Demina M.V. Polygons of differential equation for finding exact solutions. Chaos Soliton Fract 33 (2007) 1480-1496
    • (2007) Chaos Soliton Fract , vol.33 , pp. 1480-1496
    • Kudryashov, N.A.1    Demina, M.V.2
  • 25
    • 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. Regular Chaotic Dyn 13 (2008) 234-238
    • (2008) Regular Chaotic Dyn , vol.13 , pp. 234-238
    • Kudryashov, N.A.1
  • 26
    • 54049115011 scopus 로고    scopus 로고
    • Extended simplest equation method for nonlinear differential equations
    • Kudryashov N.A., and Loguinova N.B. Extended simplest equation method for nonlinear differential equations. Appl Math Comput 205 (2008) 396-402
    • (2008) Appl Math Comput , vol.205 , pp. 396-402
    • Kudryashov, N.A.1    Loguinova, N.B.2
  • 27
    • 0009295586 scopus 로고
    • Exact solutions for some nonlinear equations
    • Lan H., and Wang K. Exact solutions for some nonlinear equations. Phys Lett A 137 (1989) 369-373
    • (1989) Phys Lett A , vol.137 , pp. 369-373
    • Lan, H.1    Wang, K.2
  • 28
    • 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
  • 29
    • 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 Scripta 54 (1996) 563-568
    • (1996) Phys Scripta , vol.54 , pp. 563-568
    • Malfliet, W.1    Hereman, W.2
  • 30
    • 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
  • 31
    • 37549033511 scopus 로고    scopus 로고
    • ′ / G-expansion method and evolution equations in mathematical physics
    • ′ / G-expansion method and evolution equations in mathematical physics. Phys Lett A 372 4 (2008) 417
    • (2008) Phys Lett A , vol.372 , Issue.4 , pp. 417
    • Wang, M.L.1    Li, X.2    Zhang, J.3
  • 32
    • 41949137395 scopus 로고    scopus 로고
    • ′ / G-expansion method for nonlinear evolution equations
    • ′ / G-expansion method for nonlinear evolution equations. Phys Lett A (2008) 3400-3406
    • (2008) Phys Lett A , pp. 3400-3406
    • Bekir, A.1
  • 33
    • 42749091472 scopus 로고    scopus 로고
    • ′ / G-expansion method and its applications
    • ′ / G-expansion method and its applications. Phys Lett A 372 (2008) 3653-3658
    • (2008) Phys Lett A , vol.372 , pp. 3653-3658
    • Zhang, J.1    Wei, X.2    Lu, Y.3
  • 34
    • 34248229664 scopus 로고    scopus 로고
    • The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
    • Wazwaz A.M. The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. Appl Math Comput 188 (2007) 1467-1475
    • (2007) Appl Math Comput , vol.188 , pp. 1467-1475
    • Wazwaz, A.M.1
  • 35
    • 34249777548 scopus 로고    scopus 로고
    • The extended tanh method and its applications for solving nonlinear physical models
    • Abdou M.A. The extended tanh method and its applications for solving nonlinear physical models. Appl Math Comput 199 (2007) 988-996
    • (2007) Appl Math Comput , vol.199 , pp. 988-996
    • Abdou, M.A.1
  • 36
    • 58349105753 scopus 로고    scopus 로고
    • A modified tanh-coth method for solving the general Burgers-Fisher and the Kuramoto-Sivashinsky equations
    • Wazzan L. A modified tanh-coth method for solving the general Burgers-Fisher and the Kuramoto-Sivashinsky equations. Commun Nonlinear Sci Numer Simulat 14 (2009) 2642-2652
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 2642-2652
    • Wazzan, L.1
  • 37
    • 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 Soliton Fract 30 (2006) 700-708
    • (2006) Chaos Soliton Fract , vol.30 , pp. 700-708
    • He, J.H.1    Wu, X.H.2
  • 38
    • 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 Soliton Fract 34 (2007) 1421-1429
    • (2007) Chaos Soliton Fract , vol.34 , pp. 1421-1429
    • He, J.H.1    Abdou, M.A.2
  • 39
    • 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
  • 40
    • 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
  • 41
    • 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
  • 43
    • 38949127273 scopus 로고    scopus 로고
    • Generalized multiple Riccati equations rational expansion method with symbolic computation to construct exact complex solutions of nonlinear partial differential equations
    • Li W., and Zhang H. Generalized multiple Riccati equations rational expansion method with symbolic computation to construct exact complex solutions of nonlinear partial differential equations. Appl Math Comput 197 (2008) 288-296
    • (2008) Appl Math Comput , vol.197 , pp. 288-296
    • Li, W.1    Zhang, H.2
  • 44
    • 67649342557 scopus 로고    scopus 로고
    • Exp-function method for constructing exact solutions of Sharma-Tasso-Olver equation
    • 10.1016/j.chaos.2008.09.003
    • Erbas B., and Yusufoǧlu E. Exp-function method for constructing exact solutions of Sharma-Tasso-Olver equation. Chaos Soliton Fract (2008) 10.1016/j.chaos.2008.09.003
    • (2008) Chaos Soliton Fract
    • Erbas, B.1    Yusufoǧlu, E.2
  • 45
    • 41849090442 scopus 로고    scopus 로고
    • Application of the Exp-function method to high-dimensional nonlinear evolution equation
    • Zhang S. Application of the Exp-function method to high-dimensional nonlinear evolution equation. Chaos Soliton Fract 38 (2008) 270-276
    • (2008) Chaos Soliton Fract , vol.38 , pp. 270-276
    • Zhang, S.1
  • 46
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves
    • Korteweg D.J., and de Vries G. On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves. Philos Mag 39 (1895) 422-443
    • (1895) Philos Mag , vol.39 , pp. 422-443
    • Korteweg, D.J.1    de Vries, G.2
  • 47
    • 56049095456 scopus 로고    scopus 로고
    • On "new traveling wave solutions of the KdV and the KdV - Burgers equations
    • Kudryashov N.A. On "new traveling wave solutions of the KdV and the KdV - Burgers equations. Commun Nonlinear Sci Numer Simulat 14 (2009) 1891-1900
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 1891-1900
    • Kudryashov, N.A.1
  • 48
    • 67349247485 scopus 로고    scopus 로고
    • Analytic study on the higher order Ito equations: new solitary wave solutions using the Exp-function method
    • 10.1016/j.chaos.2008.08.023
    • Khani F. Analytic study on the higher order Ito equations: new solitary wave solutions using the Exp-function method. Chaos Soliton Fract (2008) 10.1016/j.chaos.2008.08.023
    • (2008) Chaos Soliton Fract
    • Khani, F.1
  • 49
    • 55549089262 scopus 로고    scopus 로고
    • Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miva equation via the Exp-function method
    • Öziş T., and Aslan I. Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miva equation via the Exp-function method. Phys Lett A 372 (2008) 7011-7015
    • (2008) Phys Lett A , vol.372 , pp. 7011-7015
    • Öziş, T.1    Aslan, I.2
  • 50
    • 57649083121 scopus 로고    scopus 로고
    • Approximate general and explicit solutions of nonlinear BBMB equations by Exp-function method
    • 10.1016/j.apm.2008.03.005
    • Ganji Z.Z., Ganji D.D., and Bararnia H. Approximate general and explicit solutions of nonlinear BBMB equations by Exp-function method. Appl Math Model (2008) 10.1016/j.apm.2008.03.005
    • (2008) Appl Math Model
    • Ganji, Z.Z.1    Ganji, D.D.2    Bararnia, H.3
  • 51
    • 67349205096 scopus 로고    scopus 로고
    • Exact solutions of the KdV - Burgers equation by Exp-function method
    • 10.1016/J.chaos. 2008.04.038
    • Soliman A.A. Exact solutions of the KdV - Burgers equation by Exp-function method. Chaos Soliton Fract (2008) 10.1016/J.chaos. 2008.04.038
    • (2008) Chaos Soliton Fract
    • Soliman, A.A.1
  • 52
    • 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
  • 54
    • 39749117350 scopus 로고    scopus 로고
    • Generalized solitonary and periodic solutions for nonlinear partial differential equations by the Exp-function method
    • 10.1007/s1071-007-9250-1
    • Abdou M.A. Generalized solitonary and periodic solutions for nonlinear partial differential equations by the Exp-function method. Nonlinear Dyn 52 (2008) 1-9 10.1007/s1071-007-9250-1
    • (2008) Nonlinear Dyn , vol.52 , pp. 1-9
    • Abdou, M.A.1
  • 55
    • 48049096604 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the generalized (1 + 1)-dimensional and the generalized (2 + 1)-dimensional Ito equations
    • Wazwaz A.M. Multiple-soliton solutions for the generalized (1 + 1)-dimensional and the generalized (2 + 1)-dimensional Ito equations. Appl Math Comput 202 (2008) 840-849
    • (2008) Appl Math Comput , vol.202 , pp. 840-849
    • Wazwaz, A.M.1
  • 56
    • 18944400520 scopus 로고
    • New similarity reductions of the Boussinesq equation
    • Clarkson P.A., and Kruskal M.D. New similarity reductions of the Boussinesq equation. J Math Phys 30 (1989) 2201-2213
    • (1989) J Math Phys , vol.30 , pp. 2201-2213
    • Clarkson, P.A.1    Kruskal, M.D.2
  • 57
    • 55649084357 scopus 로고    scopus 로고
    • Solutions of the Cahn-Hillard equation
    • 10.1016/j.camwa.2008.07.007
    • Ugurlu Y., and Kaya D. Solutions of the Cahn-Hillard equation. Comput Math Appl (2008) 10.1016/j.camwa.2008.07.007
    • (2008) Comput Math Appl
    • Ugurlu, Y.1    Kaya, D.2
  • 58
    • 55549105751 scopus 로고    scopus 로고
    • On travelling wave solutions to combined KdV-mKdV and modified Burgers - KdV equation
    • Bekir A. On travelling wave solutions to combined KdV-mKdV and modified Burgers - KdV equation. Commun Nonlinear Sci Numer Simulat 14 (2009) 1038-1042
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 1038-1042
    • Bekir, A.1
  • 59
    • 41149150935 scopus 로고    scopus 로고
    • Applications of the extended tanh method for coupled nonlinear evolution equations
    • Bekir A. Applications of the extended tanh method for coupled nonlinear evolution equations. Commun Nonlinear Sci Numer Simulat 13 (2008) 1748-1757
    • (2008) Commun Nonlinear Sci Numer Simulat , vol.13 , pp. 1748-1757
    • Bekir, A.1
  • 60
    • 9644255681 scopus 로고    scopus 로고
    • Symbolic computation in nonlinear evolution equation: application to (3 + 1)-dimensional Kadomttsev-Petviasvili equation
    • Xie F., Zhang Y., and Lü Z. Symbolic computation in nonlinear evolution equation: application to (3 + 1)-dimensional Kadomttsev-Petviasvili equation. Chaos Soliton Fract 24 (2005) 257-263
    • (2005) Chaos Soliton Fract , vol.24 , pp. 257-263
    • Xie, F.1    Zhang, Y.2    Lü, Z.3
  • 61
    • 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. Symbolic computation and new families of exact non-travelling wave solutions of (2 + 1)-dimensional Konopelchenko-Dubrovsky equations. Chaos Soliton Fract 31 (2007) 951-959
    • (2007) Chaos Soliton Fract , vol.31 , pp. 951-959
    • Zhang, S.1
  • 62
    • 34248151886 scopus 로고    scopus 로고
    • New solitons and kinks solutions to the Sharma-Tasso-Olver equation
    • Wazwaz A.M. New solitons and kinks solutions to the Sharma-Tasso-Olver equation. Appl Math Comput 188 (2007) 1205-1213
    • (2007) Appl Math Comput , vol.188 , pp. 1205-1213
    • Wazwaz, A.M.1
  • 63
    • 33751530880 scopus 로고    scopus 로고
    • New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations
    • Wazwaz A.M. New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations. Appl Math Comput 182 (2006) 164250
    • (2006) Appl Math Comput , vol.182 , pp. 164250
    • Wazwaz, A.M.1
  • 64
    • 0000507179 scopus 로고
    • Persistent Propagation of concentration waves in dissipative media far from thermal equlibrium
    • Kuramoto Y., and Tsuzuki T. Persistent Propagation of concentration waves in dissipative media far from thermal equlibrium. Prog Theor Phys 55 2 (1976) 356-369
    • (1976) Prog Theor Phys , vol.55 , Issue.2 , pp. 356-369
    • Kuramoto, Y.1    Tsuzuki, T.2
  • 65
    • 0037774603 scopus 로고    scopus 로고
    • New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation
    • Chen H., and Zhang H. New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation. Chaos Soliton Fract 19 (2004) 71-76
    • (2004) Chaos Soliton Fract , vol.19 , pp. 71-76
    • Chen, H.1    Zhang, H.2
  • 66
    • 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
  • 67
    • 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
  • 68
    • 34548631824 scopus 로고    scopus 로고
    • New application of Exp-function method for improved Boussinesq equation
    • Abdou M.A., Soliman A.A., and El-Basony S.T. 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    Soliman, A.A.2    El-Basony, S.T.3
  • 69
    • 56049127915 scopus 로고    scopus 로고
    • Solitary wave solutions of two nonlinear physical models by tanh-coth method
    • Bekir A., and Cevikel A.C. Solitary wave solutions of two nonlinear physical models by tanh-coth method. Commun Nonlinear Sci Numer Simulat 14 (2009) 1804-1809
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 1804-1809
    • Bekir, A.1    Cevikel, A.C.2
  • 70
    • 42749088097 scopus 로고    scopus 로고
    • A novel approach for solving the Fisher equation using Exp-function method
    • Öziş T., and Köroǧlu C. A novel approach for solving the Fisher equation using Exp-function method. Phys Lett A 372 (2008) 3836-3840
    • (2008) Phys Lett A , vol.372 , pp. 3836-3840
    • Öziş, T.1    Köroǧlu, C.2
  • 71
    • 40549129324 scopus 로고    scopus 로고
    • Application of Exp-function method to the generalized Burgers-Huxley equation
    • Chun C. Application of Exp-function method to the generalized Burgers-Huxley equation. J Phys Conf Ser 96 (2008) 012217
    • (2008) J Phys Conf Ser , vol.96 , pp. 012217
    • Chun, C.1
  • 72
    • 8744316856 scopus 로고    scopus 로고
    • Exact solutions of the Burgers-Huxley equation
    • Efimova 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
    • Efimova, O.Yu.1    Kudryashov, N.A.2
  • 73
    • 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
  • 74
    • 40549140406 scopus 로고    scopus 로고
    • Exp-function method for Klein-Gordon equation with quadratic nonlinearity
    • Zhang S. Exp-function method for Klein-Gordon equation with quadratic nonlinearity. J Phys Conf Ser 96 (2008) 012002
    • (2008) J Phys Conf Ser , vol.96 , pp. 012002
    • Zhang, S.1
  • 75
    • 58149477049 scopus 로고    scopus 로고
    • Exp-function method for solving Kuramoto-Sivashinsky and Boussinesq equations
    • 10.1007/s12190-008-0083-y
    • Noor M.A., Mohyud-Din S.T., and Waheed A. Exp-function method for solving Kuramoto-Sivashinsky and Boussinesq equations. J Appl Math Comput (2008) 10.1007/s12190-008-0083-y
    • (2008) J Appl Math Comput
    • Noor, M.A.1    Mohyud-Din, S.T.2    Waheed, A.3
  • 76
    • 57549110604 scopus 로고    scopus 로고
    • New exact solutions of the (3 + 1)-dimensional Burgers system
    • 10.1016/j.physleta.2008.11.018
    • Dai C.Q., and Wang Y.Y. New exact solutions of the (3 + 1)-dimensional Burgers system. Phys Lett A (2008) 10.1016/j.physleta.2008.11.018
    • (2008) Phys Lett A
    • Dai, C.Q.1    Wang, Y.Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.