메뉴 건너뛰기




Volumn 14, Issue 6, 2001, Pages 1433-1452

Decomposition of the (2 + 1)-dimensional Gardner equation and its quasi-periodic solutions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035511439     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/14/6/302     Document Type: Article
Times cited : (118)

References (33)
  • 4
    • 85008279103 scopus 로고
    • Solitons and infinite dimensional Lie algebras
    • Jimbo M and Miwa T 1983 Solitons and infinite dimensional Lie algebras Publ. RIMS Kyoto Univ. 19 943-1001
    • (1983) Publ. RIMS Kyoto Univ. , vol.19 , pp. 943-1001
    • Jimbo, M.1    Miwa, T.2
  • 5
    • 0003058680 scopus 로고
    • Classical integrable systems generated through nonlinearization of eigenvalue problems
    • Berlin: Springer
    • Cao C W and Geng X G 1990 Classical integrable systems generated through nonlinearization of eigenvalue problems Nonlinear Physics (Research Reports in Physics) (Berlin: Springer) pp 68-78
    • (1990) Nonlinear Physics (Research Reports in Physics) , pp. 68-78
    • Cao, C.W.1    Geng, X.G.2
  • 6
    • 0001176461 scopus 로고
    • Nonlinearization of the Lax system for AKNS hierarchy
    • Cao C W 1990 Nonlinearization of the Lax system for AKNS hierarchy Sci. China A 33 528-36
    • (1990) Sci. China A , vol.33 , pp. 528-536
    • Cao, C.W.1
  • 7
    • 36149029754 scopus 로고
    • C Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy
    • Cao C W and Geng X G 1990 C Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy J. Phys. A: Math. Gen. 23 4117-25
    • (1990) J. Phys. A: Math. Gen. , vol.23 , pp. 4117-4125
    • Cao, C.W.1    Geng, X.G.2
  • 8
    • 0002329475 scopus 로고
    • (1 + 1)-dimensional integrable systems as symmetry constraints of (2 + 1)-dimensional systems
    • Bonopelchenko B, Sidorenko J and Strampp W 1991 (1 + 1)-dimensional integrable systems as symmetry constraints of (2+ 1)-dimensional systems Phys. Lett. A 157 17-21
    • (1991) Phys. Lett. A , vol.157 , pp. 17-21
    • Bonopelchenko, B.1    Sidorenko, J.2    Strampp, W.3
  • 9
    • 0002447196 scopus 로고
    • The constraint of the Kadomtsev-Petviashvili equation and its special solutions
    • Cheng Y and Li Y S 1991 The constraint of the Kadomtsev-Petviashvili equation and its special solutions Phys. Lett. A 157 22-6
    • (1991) Phys. Lett. A , vol.157 , pp. 22-26
    • Cheng, Y.1    Li, Y.S.2
  • 10
    • 48749137401 scopus 로고
    • Some new integrable nonlinear evolution equations in 2 + 1 dimensions
    • Konopelchenko B and Dubrovsky V 1984 Some new integrable nonlinear evolution equations in 2 + 1 dimensions Phys. Lett. A 102 15-7
    • (1984) Phys. Lett. A , vol.102 , pp. 15-17
    • Konopelchenko, B.1    Dubrovsky, V.2
  • 12
    • 0007187232 scopus 로고
    • A hierarchy of coupled Korteweg-de Vries equations and the normalization conditions of the Hilbert-Riemann problem
    • Levi D, Sym A and Wojciechowsk S 1983 A hierarchy of coupled Korteweg-de Vries equations and the normalization conditions of the Hilbert-Riemann problem J. Phys. A: Math. Gen. 16 2423-32
    • (1983) J. Phys. A: Math. Gen. , vol.16 , pp. 2423-2432
    • Levi, D.1    Sym, A.2    Wojciechowsk, S.3
  • 13
    • 33947180234 scopus 로고
    • A symmetric approach to the classification of nonlinear equations, complete lists of integrable systems
    • Mikhailov A V, Shabat A B and Yamilov R I 1987 A symmetric approach to the classification of nonlinear equations, complete lists of integrable systems Russian Math. Surv. 41 1-63
    • (1987) Russian Math. Surv. , vol.41 , pp. 1-63
    • Mikhailov, A.V.1    Shabat, A.B.2    Yamilov, R.I.3
  • 14
    • 0002800178 scopus 로고
    • Extension of the module of invertible transformations, classification of integrable systems
    • Mikhailov A V, Shabat A B and Yamilov R I 1988 Extension of the module of invertible transformations, classification of integrable systems Commun. Math. Phys. 115 1-19
    • (1988) Commun. Math. Phys. , vol.115 , pp. 1-19
    • Mikhailov, A.V.1    Shabat, A.B.2    Yamilov, R.I.3
  • 16
    • 0032222021 scopus 로고    scopus 로고
    • An alternative approach to algebro-geometric solutions of the AKNS hierarchy
    • Gesztesy F and Ratnaseelan R 1998 An alternative approach to algebro-geometric solutions of the AKNS hierarchy Rev. Math. Phys. 10 345-91
    • (1998) Rev. Math. Phys. , vol.10 , pp. 345-391
    • Gesztesy, F.1    Ratnaseelan, R.2
  • 18
    • 84913921727 scopus 로고
    • Nonlinear equations of Korteweg-de Vries type, finite-zone linear operators and Abelian varieties
    • Dubrovin B A, Mateev V B and Novikov S P 1976 Nonlinear equations of Korteweg-de Vries type, finite-zone linear operators and Abelian varieties Russ. Math. Surv. 31 55-136
    • (1976) Russ. Math. Surv. , vol.31 , pp. 55-136
    • Dubrovin, B.A.1    Mateev, V.B.2    Novikov, S.P.3
  • 19
    • 0000487511 scopus 로고
    • On quasi-periodic solutions of the field equation of the classical massive Thirring model
    • Date E 1978 On quasi-periodic solutions of the field equation of the classical massive Thirring model Prog. Theor. Phys. 59 265-73
    • (1978) Prog. Theor. Phys. , vol.59 , pp. 265-273
    • Date, E.1
  • 20
    • 36749107839 scopus 로고
    • Spectral theory for the periodic sine-Gordon equation: A concrete viewpoint
    • Forest M G and Mclaughlin D W 1982 Spectral theory for the periodic sine-Gordon equation: a concrete viewpoint J. Math. Phys. 23 1248-77
    • (1982) J. Math. Phys. , vol.23 , pp. 1248-1277
    • Forest, M.G.1    Mclaughlin, D.W.2
  • 21
    • 0000456901 scopus 로고
    • Study of quasiperiodic solutions of nonlinear Schrödinger equation and the nonlinear modulational instability
    • Tracy E R, Chen H H and Lee Y C 1984 Study of quasiperiodic solutions of nonlinear Schrödinger equation and the nonlinear modulational instability Phys. Rev. Lett. 53 218-21
    • (1984) Phys. Rev. Lett. , vol.53 , pp. 218-221
    • Tracy, E.R.1    Chen, H.H.2    Lee, Y.C.3
  • 22
    • 84972582970 scopus 로고
    • Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation
    • Previato E 1985 Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation Duke Math. J. 52 329-248
    • (1985) Duke Math. J. , vol.52 , pp. 329-1248
    • Previato, E.1
  • 23
    • 0031518253 scopus 로고    scopus 로고
    • The finite-band solution of Jaulent-Miodek equation
    • Zhou R G 1997 The finite-band solution of Jaulent-Miodek equation J. Math. Phys. 38 2335-546
    • (1997) J. Math. Phys. , vol.38 , pp. 2335-2546
    • Zhou, R.G.1
  • 24
    • 0001804145 scopus 로고    scopus 로고
    • A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy
    • Gesztesy F and Weikard R 1998 A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy Acta Math. 181 63-108
    • (1998) Acta Math. , vol.181 , pp. 63-108
    • Gesztesy, F.1    Weikard, R.2
  • 25
    • 0033147869 scopus 로고    scopus 로고
    • Finite-band solutions of the classical Boussinesq-Burgers equations
    • Geng X G and Wu Y T 1999 Finite-band solutions of the classical Boussinesq-Burgers equations J. Math. Phys. 40 2971-82
    • (1999) J. Math. Phys. , vol.40 , pp. 2971-2982
    • Geng, X.G.1    Wu, Y.T.2
  • 26
    • 0033177320 scopus 로고    scopus 로고
    • Relation between the Kadometsev-Petviashvili equation and the confocal involutive system
    • Cao C W, Wu Y T and Geng X G 1999 Relation between the Kadometsev-Petviashvili equation and the confocal involutive system J. Math. Phys. 40 3948-70
    • (1999) J. Math. Phys. , vol.40 , pp. 3948-3970
    • Cao, C.W.1    Wu, Y.T.2    Geng, X.G.3
  • 27
    • 0033584758 scopus 로고    scopus 로고
    • From the special 2 + 1 Toda lattice to the Kadomtsev-Petviashvili equation
    • Cao C W, Geng X G and Wu Y T 1999 From the special 2 + 1 Toda lattice to the Kadomtsev-Petviashvili equation J. Phys. A: Math. Gen. 32 8059-78
    • (1999) J. Phys. A: Math. Gen. , vol.32 , pp. 8059-8078
    • Cao, C.W.1    Geng, X.G.2    Wu, Y.T.3
  • 28
    • 0033591084 scopus 로고    scopus 로고
    • Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation
    • Geng X G, Wu Y T and Cao C W 1999 Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation J. Phys. A: Math. Gen. 32 3733-42
    • (1999) J. Phys. A: Math. Gen. , vol.32 , pp. 3733-3742
    • Geng, X.G.1    Wu, Y.T.2    Cao, C.W.3
  • 29
    • 0034342190 scopus 로고    scopus 로고
    • Algebro-geometric solutions of (2 + 1)-dimensional coupled modified Kadometsev-Petviashvili equations
    • Geng X G and Dai H H 2000 Algebro-geometric solutions of (2 + 1)-dimensional coupled modified Kadometsev-Petviashvili equations J. Math. Phys. 41 337-48
    • (2000) J. Math. Phys. , vol.41 , pp. 337-348
    • Geng, X.G.1    Dai, H.H.2
  • 30
    • 0007250441 scopus 로고
    • Inverse spectral transform for the (2 + 1)-dimensional Gardner equation
    • Konopelchenko B 1991 Inverse spectral transform for the (2 + 1)-dimensional Gardner equation Inverse Problems 7 739-53
    • (1991) Inverse Problems , vol.7 , pp. 739-753
    • Konopelchenko, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.