메뉴 건너뛰기




Volumn 215, Issue 8, 2009, Pages 2835-2842

Direct search for exact solutions to the nonlinear Schrödinger equation

Author keywords

Periodic solution; Rational solution; Soliton solution; Symmetry algebra; The nonlinear Schr dinger equation

Indexed keywords

BIFURCATION PHENOMENA; DINGER EQUATION; DIRECT SEARCH; EXACT SOLUTION; EXPONENTIAL FUNCTIONS; LIE POINT SYMMETRIES; PERIODIC SOLUTION; RATIONAL FUNCTION; RATIONAL SOLUTION; SOLITON SOLUTION; SOLUTION PROCESS; SYMMETRY ALGEBRA; TRIGONOMETRIC FUNCTIONS;

EID: 70449535523     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.09.024     Document Type: Article
Times cited : (182)

References (41)
  • 3
    • 0002557939 scopus 로고
    • Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media
    • (translated from Zh. Èksper. Teoret. Fiz. 61 (1971) 118-134)
    • Zakharov V.E., and Shabat A.B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34 (1972) 62-69 (translated from Zh. Èksper. Teoret. Fiz. 61 (1971) 118-134)
    • (1972) Sov. Phys. JETP , vol.34 , pp. 62-69
    • Zakharov, V.E.1    Shabat, A.B.2
  • 4
    • 0000169358 scopus 로고
    • Interaction between solitons in a stable medium
    • (translated from Zh. Èksper. Teoret. Fiz. 64 (1973) 1627-1639)
    • Zakharov V.E., and Shabat A.B. Interaction between solitons in a stable medium. Sov. Phys. JETP 37 (1973) 823-828 (translated from Zh. Èksper. Teoret. Fiz. 64 (1973) 1627-1639)
    • (1973) Sov. Phys. JETP , vol.37 , pp. 823-828
    • Zakharov, V.E.1    Shabat, A.B.2
  • 5
    • 0040621774 scopus 로고
    • General N-soliton solution of the AKNS class on arbitrary background
    • Neugebauer G., and Meinel R. General N-soliton solution of the AKNS class on arbitrary background. Phys. Lett. A 100 (1984) 467-470
    • (1984) Phys. Lett. A , vol.100 , pp. 467-470
    • Neugebauer, G.1    Meinel, R.2
  • 8
    • 0004799048 scopus 로고
    • Explicit formulas for solutions of a nonlinear Schrödinger equation
    • 1051
    • Its A.R., and Kotljarov V.P. Explicit formulas for solutions of a nonlinear Schrödinger equation. Dokl. Akad. Nauk Ukrain. SSR Ser. A 11 (1976) 965-968 1051
    • (1976) Dokl. Akad. Nauk Ukrain. SSR Ser. A , vol.11 , pp. 965-968
    • Its, A.R.1    Kotljarov, V.P.2
  • 9
    • 0003006528 scopus 로고
    • The perturbed plane-wave solutions of the cubic Schrödinger equation
    • Ma Y.C. The perturbed plane-wave solutions of the cubic Schrödinger equation. Stud. Appl. Math. 60 (1979) 43-58
    • (1979) Stud. Appl. Math. , vol.60 , pp. 43-58
    • Ma, Y.C.1
  • 10
    • 0001951716 scopus 로고
    • nonlinear Schrödinger equations and their solutions
    • Peregrine D.H., and waves W. nonlinear Schrödinger equations and their solutions. J. Austral. Math. Soc. Ser. B 25 (1983) 16-43
    • (1983) J. Austral. Math. Soc. Ser. B , vol.25 , pp. 16-43
    • Peregrine, D.H.1    waves, W.2
  • 11
    • 11744388723 scopus 로고
    • First-order exact solutions of the nonlinear Schrödinger equation
    • (translated from Teoret. Mat. Fiz. 72 (1987) 183-196)
    • Akhmediev N.N., Eleonskii{dotless}̌ V.M., and Kulagin N.E. First-order exact solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 72 (1987) 809-818 (translated from Teoret. Mat. Fiz. 72 (1987) 183-196)
    • (1987) Theor. Math. Phys. , vol.72 , pp. 809-818
    • Akhmediev, N.N.1    Eleonskiǐ, V.M.2    Kulagin, N.E.3
  • 12
    • 0007603790 scopus 로고
    • Multiple pole solutions of the nonlinear Schrödinger equation
    • Olmedilla E. Multiple pole solutions of the nonlinear Schrödinger equation. Physica D 25 (1987) 330-346
    • (1987) Physica D , vol.25 , pp. 330-346
    • Olmedilla, E.1
  • 13
    • 36149035438 scopus 로고
    • General soliton solutions of an n-dimensional nonlinear Schrödinger equation
    • Hai W.H. General soliton solutions of an n-dimensional nonlinear Schrödinger equation. J. Phys. A: Math. Gen. 25 (1992) L515-L519
    • (1992) J. Phys. A: Math. Gen. , vol.25
    • Hai, W.H.1
  • 14
    • 0038374490 scopus 로고    scopus 로고
    • A new approach to the cubic Schrödinger equation: an application of the decomposition technique
    • Khuri S.A. A new approach to the cubic Schrödinger equation: an application of the decomposition technique. Appl. Math. Comput. 97 (1998) 251-254
    • (1998) Appl. Math. Comput. , vol.97 , pp. 251-254
    • Khuri, S.A.1
  • 15
    • 0040117080 scopus 로고    scopus 로고
    • A note on slowly decaying solutions of the defocusing nonlinear Schrödinger equation
    • Barran S., and Kovalyov M. A note on slowly decaying solutions of the defocusing nonlinear Schrödinger equation. J. Phys. A: Math. Gen. 32 (1999) 6121-6125
    • (1999) J. Phys. A: Math. Gen. , vol.32 , pp. 6121-6125
    • Barran, S.1    Kovalyov, M.2
  • 16
    • 0039741902 scopus 로고    scopus 로고
    • The eigenvalue problem for the focusing nonlinear Schrödinger equation: new solvable cases
    • Tovbis A., and Venakides S. The eigenvalue problem for the focusing nonlinear Schrödinger equation: new solvable cases. Physica D 146 (2000) 150-164
    • (2000) Physica D , vol.146 , pp. 150-164
    • Tovbis, A.1    Venakides, S.2
  • 17
    • 0038373223 scopus 로고    scopus 로고
    • An analytical solution to the dissipative nonlinear Schrödinger equation
    • Demiray H. An analytical solution to the dissipative nonlinear Schrödinger equation. Appl. Math. Comput. 145 (2003) 179-184
    • (2003) Appl. Math. Comput. , vol.145 , pp. 179-184
    • Demiray, H.1
  • 19
    • 0347985401 scopus 로고    scopus 로고
    • A complex tanh-function method applied to nonlinear equations of Schrödinger type
    • Khuri S.A. A complex tanh-function method applied to nonlinear equations of Schrödinger type. Chaos Soliton. Fract. 20 (2004) 1037-1040
    • (2004) Chaos Soliton. Fract. , vol.20 , pp. 1037-1040
    • Khuri, S.A.1
  • 20
    • 31644440712 scopus 로고    scopus 로고
    • A numerical solution and an exact explicit solution of the NLS equation
    • El-Sayed S.M., and Kaya D. A numerical solution and an exact explicit solution of the NLS equation. Appl. Math. Comput. 172 (2006) 1315-1322
    • (2006) Appl. Math. Comput. , vol.172 , pp. 1315-1322
    • El-Sayed, S.M.1    Kaya, D.2
  • 21
    • 33644522735 scopus 로고    scopus 로고
    • Reliable analysis for nonlinear Schrödinger equations with a cubic nonlinearity and a power law nonlinearity
    • Wazwaz A.M. Reliable analysis for nonlinear Schrödinger equations with a cubic nonlinearity and a power law nonlinearity. Math. Comput. Model. 43 (2006) 178-184
    • (2006) Math. Comput. Model. , vol.43 , pp. 178-184
    • Wazwaz, A.M.1
  • 22
    • 41449093551 scopus 로고    scopus 로고
    • Exact solutions to the focusing nonlinear Schrödinger equation
    • Aktosun T., Demontis F., and van der Mee C. Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Probl. 23 (2007) 2171-2195
    • (2007) Inverse Probl. , vol.23 , pp. 2171-2195
    • Aktosun, T.1    Demontis, F.2    van der Mee, C.3
  • 23
    • 40649100751 scopus 로고    scopus 로고
    • A study on linear and nonlinear Schrödinger equations by the variational iteration method
    • Wazwaz A.M. A study on linear and nonlinear Schrödinger equations by the variational iteration method. Chaos Soliton. Fract. 37 (2008) 1136-1142
    • (2008) Chaos Soliton. Fract. , vol.37 , pp. 1136-1142
    • Wazwaz, A.M.1
  • 24
    • 41849137278 scopus 로고    scopus 로고
    • Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation
    • Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation. Chaos Soliton. Fract. 38 (2008) 209-212
    • (2008) Chaos Soliton. Fract. , vol.38 , pp. 209-212
    • Öziş, T.1    Yildirim, A.2
  • 25
    • 50249151883 scopus 로고    scopus 로고
    • New exact complex travelling wave solutions to nonlinear Schrödinger (NLS) equation
    • Zhang H.Q. New exact complex travelling wave solutions to nonlinear Schrödinger (NLS) equation. Commun. Nonlinear Sci. Numer. Simulat. 14 (2009) 668-673
    • (2009) Commun. Nonlinear Sci. Numer. Simulat. , vol.14 , pp. 668-673
    • Zhang, H.Q.1
  • 26
    • 0000862222 scopus 로고
    • Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations
    • Ma W.X. Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations. J. Math. Phys. 33 (1992) 2464-2476
    • (1992) J. Math. Phys. , vol.33 , pp. 2464-2476
    • Ma, W.X.1
  • 27
    • 33749535089 scopus 로고
    • K-symmetries and τ-symmetries of evolution equations and their Lie algebras
    • Ma W.X. K-symmetries and τ-symmetries of evolution equations and their Lie algebras. J. Phys. A: Math. Gen. 23 (1990) 2707-2716
    • (1990) J. Phys. A: Math. Gen. , vol.23 , pp. 2707-2716
    • Ma, W.X.1
  • 29
    • 0000541374 scopus 로고
    • On three dimensional packets of surface waves
    • Davey A., and Stewartson K. On three dimensional packets of surface waves. Proc. Roy. Soc. A 338 (1974) 101-110
    • (1974) Proc. Roy. Soc. A , vol.338 , pp. 101-110
    • Davey, A.1    Stewartson, K.2
  • 30
    • 68349126919 scopus 로고    scopus 로고
    • A class of exact solutions of the generalized nonautonomous nonlinear Schrödinger equation
    • Zhang Y., Yao C.Z., Cai X.N., and Xu H.X. A class of exact solutions of the generalized nonautonomous nonlinear Schrödinger equation. Rep. Math. Phys. 63 (2009) 427-439
    • (2009) Rep. Math. Phys. , vol.63 , pp. 427-439
    • Zhang, Y.1    Yao, C.Z.2    Cai, X.N.3    Xu, H.X.4
  • 31
    • 70449535065 scopus 로고    scopus 로고
    • Wronskian solutions of a generalized nonautonomous nonlinear Schrödinger equation
    • preprint
    • Y. Zhang, H.X. Xu, C.Z. Yao, X.N. Cai, Wronskian solutions of a generalized nonautonomous nonlinear Schrödinger equation, preprint.
    • Zhang, Y.1    Xu, H.X.2    Yao, C.Z.3    Cai, X.N.4
  • 32
    • 0037136277 scopus 로고    scopus 로고
    • Complexiton solutions to the Korteweg-de Vries equation
    • Ma W.X. Complexiton solutions to the Korteweg-de Vries equation. Phys. Lett. A 301 (2002) 35-44
    • (2002) Phys. Lett. A , vol.301 , pp. 35-44
    • Ma, W.X.1
  • 33
    • 18144382273 scopus 로고    scopus 로고
    • Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
    • Ma W.X., and You Y.C. Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions. Trans. Amer. Math. Soc. 357 (2005) 1753-1778
    • (2005) Trans. Amer. Math. Soc. , vol.357 , pp. 1753-1778
    • Ma, W.X.1    You, Y.C.2
  • 34
    • 4544353887 scopus 로고    scopus 로고
    • Complexiton solutions of the Toda lattice equation
    • Ma W.X., and Maruno K. Complexiton solutions of the Toda lattice equation. Physica A 343 (2004) 219-237
    • (2004) Physica A , vol.343 , pp. 219-237
    • Ma, W.X.1    Maruno, K.2
  • 35
    • 50949104134 scopus 로고    scopus 로고
    • Mixed rational-soliton solutions to the Toda lattice equation
    • Hindawi Publ. Corp., New York
    • Ma W.X. Mixed rational-soliton solutions to the Toda lattice equation. Differential & Difference Equations and Applications (2006), Hindawi Publ. Corp., New York 711-720
    • (2006) Differential & Difference Equations and Applications , pp. 711-720
    • Ma, W.X.1
  • 36
    • 33947640521 scopus 로고    scopus 로고
    • Wronskian solutions of the Boussinesq equation - solitons, negatrons, positions and complexitons
    • Li C.X., Ma W.X., Liu X.J., and Zeng Y.B. Wronskian solutions of the Boussinesq equation - solitons, negatrons, positions and complexitons. Inverse Probl. 23 (2007) 279-296
    • (2007) Inverse Probl. , vol.23 , pp. 279-296
    • Li, C.X.1    Ma, W.X.2    Liu, X.J.3    Zeng, Y.B.4
  • 37
    • 63449113626 scopus 로고    scopus 로고
    • A second Wronskian formulation of the Boussinesq equation
    • Ma W.X., He J.S., and Li C.X. A second Wronskian formulation of the Boussinesq equation. Nonlinear Anal. 70 (2009) 4245-4258
    • (2009) Nonlinear Anal. , vol.70 , pp. 4245-4258
    • Ma, W.X.1    He, J.S.2    Li, C.X.3
  • 38
    • 50949109194 scopus 로고    scopus 로고
    • An application of the Casoratian technique to the 2D Toda lattice equation
    • Ma W.X. An application of the Casoratian technique to the 2D Toda lattice equation. Mod. Phys. Lett. B 22 (2008) 1815-1825
    • (2008) Mod. Phys. Lett. B , vol.22 , pp. 1815-1825
    • Ma, W.X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.