메뉴 건너뛰기




Volumn 354, Issue 1713, 1996, Pages 1807-1835

Symmetries and exact solutions of a (2 + 1)-dimensional sine-Gordon system

Author keywords

[No Author keywords available]

Indexed keywords


EID: 3142603472     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1996.0079     Document Type: Article
Times cited : (39)

References (59)
  • 1
    • 0002004721 scopus 로고
    • Solitons, nonlinear evolution equations and inverse scattering
    • Cambridge University Press
    • Ablowitz, M. J. & Clarkson, P. A. 1991 Solitons, nonlinear evolution equations and inverse scattering (LMS Lecture Notes in Mathematics, vol. 149. Cambridge University Press.
    • (1991) LMS Lecture Notes in Mathematics , vol.149
    • Ablowitz, M.J.1    Clarkson, P.A.2
  • 2
    • 0001231291 scopus 로고
    • Nonlinear evolution equations - Two and three dimensions
    • Ablowitz, M. J. & Haberman, R. 1975 Nonlinear evolution equations - two and three dimensions. Phys. Rev. Lett. 35, 1185-1188.
    • (1975) Phys. Rev. Lett. , vol.35 , pp. 1185-1188
    • Ablowitz, M.J.1    Haberman, R.2
  • 4
    • 36849114318 scopus 로고
    • Coherent pulse propagation, a dispersive, irreversible phenomenon
    • Ablowitz, M. J., Kaup, D. J. & Newell, A. C. 1974a Coherent pulse propagation, a dispersive, irreversible phenomenon. J. Math. Phys. 15, 1852-1858.
    • (1974) J. Math. Phys. , vol.15 , pp. 1852-1858
    • Ablowitz, M.J.1    Kaup, D.J.2    Newell, A.C.3
  • 5
    • 0016369301 scopus 로고
    • The inverse scattering transform - Fourier analysis for nonlinear problems
    • Ablowitz, M. J., Kaup, D. J., Newell, A. C. & Segur, H. 1974b The inverse scattering transform - Fourier analysis for nonlinear problems. Stud. Appl. Math. 53, 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
    • 51249180884 scopus 로고
    • Nonlinear evolution equations and ordinary differential equations of Painlevé type
    • Ablowitz, M. J., Ramani, A. & Segur, H. 1978 Nonlinear evolution equations and ordinary differential equations of Painlevé type. Phys. Rev. Lett. 23, 333-338.
    • (1978) Phys. Rev. Lett. , vol.23 , pp. 333-338
    • Ablowitz, M.J.1    Ramani, A.2    Segur, H.3
  • 7
    • 36749106124 scopus 로고
    • A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
    • Ablowitz, M. J., Ramani, A. & Segur, H. 1980 A connection between nonlinear evolution equations and ordinary differential equations of P-type. I. J. Math. Phys. 21, 715-721.
    • (1980) J. Math. Phys. , vol.21 , pp. 715-721
    • Ablowitz, M.J.1    Ramani, A.2    Segur, H.3
  • 8
    • 0018495943 scopus 로고
    • Rational solutions of Painlevé equations
    • Airault, H. 1979 Rational solutions of Painlevé equations. Stud. Appl. Math. 61, 31-53.
    • (1979) Stud. Appl. Math. , vol.61 , pp. 31-53
    • Airault, H.1
  • 9
    • 36149034527 scopus 로고
    • On the Moutard transformation for integrable partial differential equations
    • Athorne, C. & Nimmo, J. J. C. 1991 On the Moutard transformation for integrable partial differential equations. Inv. Prob. 7, 809-826.
    • (1991) Inv. Prob. , vol.7 , pp. 809-826
    • Athorne, C.1    Nimmo, J.J.C.2
  • 10
    • 0000478462 scopus 로고
    • The general similarity solution of the heat equation
    • Bluman, G. W. & Cole, J. D. 1969 The general similarity solution of the heat equation. J. Math. Mech. 18, 1025-1042.
    • (1969) J. Math. Mech. , vol.18 , pp. 1025-1042
    • Bluman, G.W.1    Cole, J.D.2
  • 12
    • 51649187906 scopus 로고
    • Equations différentielles du second ordre en ÿ et du second degré en y dont l'intégrale générale est à points critiques fixès
    • Bureau, F. 1972 Equations différentielles du second ordre en ÿ et du second degré en y dont l'intégrale générale est à points critiques fixès. Ann. Mat. Pura Appl. (IV) 91, 163-281.
    • (1972) Ann. Mat. Pura Appl. (IV) , vol.91 , pp. 163-281
    • Bureau, F.1
  • 13
    • 24844478727 scopus 로고
    • The Maxwell-Bloch system with pumping and the fifth Painlevé equation
    • Burtsev, S. P. 1993 The Maxwell-Bloch system with pumping and the fifth Painlevé equation. Phys. Lett. 177A, 341-344.
    • (1993) Phys. Lett. , vol.177 A , pp. 341-344
    • Burtsev, S.P.1
  • 14
    • 0028386584 scopus 로고
    • Alternative integrable equations of nonlinear optics
    • Burtsev, S. P. & Gabitov, I. R. 1994 Alternative integrable equations of nonlinear optics. Phys. Rev. 49A, 2065-2070.
    • (1994) Phys. Rev. , vol.49 A , pp. 2065-2070
    • Burtsev, S.P.1    Gabitov, I.R.2
  • 15
    • 0008442554 scopus 로고
    • Inverse scattering method with variable spectral parameter
    • Burtsev, S. P., Mikhailov, A. V. & Zakharov, V. E. 1987 Inverse scattering method with variable spectral parameter. Theor. Math. Phys. 70, 227-240.
    • (1987) Theor. Math. Phys. , vol.70 , pp. 227-240
    • Burtsev, S.P.1    Mikhailov, A.V.2    Zakharov, V.E.3
  • 16
    • 0026222880 scopus 로고
    • The computer calculation of Lie point symmetries of large systems of differential equations
    • Champagne, B., Hereman, W. & Winternitz, P. 1991 The computer calculation of Lie point symmetries of large systems of differential equations. Comp. Phys. Commun. 66, 319-340.
    • (1991) Comp. Phys. Commun. , vol.66 , pp. 319-340
    • Champagne, B.1    Hereman, W.2    Winternitz, P.3
  • 17
    • 3142514082 scopus 로고
    • Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests
    • Clarkson, P. A. 1986a Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests. Lett. Math. Phys. 10, 297-299.
    • (1986) Lett. Math. Phys. , vol.10 , pp. 297-299
    • Clarkson, P.A.1
  • 18
    • 3142620878 scopus 로고
    • The Painlevé property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation
    • Clarkson, P. A. 1986b The Painlevé property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation. Physica 19D, 447-450.
    • (1986) Physica , vol.19 D , pp. 447-450
    • Clarkson, P.A.1
  • 19
    • 84972088211 scopus 로고
    • New exact solutions of the Boussinesq equation
    • Clarkson, P. A. 1990 New exact solutions of the Boussinesq equation. Eur. J. Appl. Math. 1, 279-300.
    • (1990) Eur. J. Appl. Math. , vol.1 , pp. 279-300
    • Clarkson, P.A.1
  • 20
    • 43949149919 scopus 로고
    • Symmetry reductions and exact solutions of a class of nonlinear heat equations
    • Clarkson, P. A. & Mansfield, E. L. 1994a Symmetry reductions and exact solutions of a class of nonlinear heat equations. Physica 70D, 250-288.
    • (1994) Physica , vol.70 D , pp. 250-288
    • Clarkson, P.A.1    Mansfield, E.L.2
  • 21
    • 0000174288 scopus 로고
    • On a shallow water wave equation
    • Clarkson, P. A. & Mansfield, E. L. 1994b On a shallow water wave equation. Nonlinearity 7, 975-1000.
    • (1994) Nonlinearity , vol.7 , pp. 975-1000
    • Clarkson, P.A.1    Mansfield, E.L.2
  • 22
    • 0028699959 scopus 로고
    • Algorithms for the nonclassical method of symmetry reductions
    • Clarkson, P. A. &; Mansfield, E. L. 1994c Algorithms for the nonclassical method of symmetry reductions. SIAM J. Appl. Math. 54, 1693-1719.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1693-1719
    • Clarkson, P.A.1    Mansfield, E.L.2
  • 23
    • 0002865557 scopus 로고
    • Painlevé classification of a class of differential equations of the second order and second degree
    • Cosgrove, C. M. & Scoufis, G. 1993 Painlevé classification of a class of differential equations of the second order and second degree. Stud. Appl. Math. 88, 25-87.
    • (1993) Stud. Appl. Math. , vol.88 , pp. 25-87
    • Cosgrove, C.M.1    Scoufis, G.2
  • 25
    • 0006170417 scopus 로고
    • The (2+1)-dimensional integrable generalization of the sine-Gordon equations. II. Localized solutions
    • Dubrovsky, V. G. & Konopelchenko, B. G. 1993 The (2+1)-dimensional integrable generalization of the sine-Gordon equations. II. Localized solutions. Inv. Prob. 9, 391-416.
    • (1993) Inv. Prob. , vol.9 , pp. 391-416
    • Dubrovsky, V.G.1    Konopelchenko, B.G.2
  • 26
    • 36749114053 scopus 로고
    • On a unified approach to transformations and elementary solutions of Painlevé equations
    • Fokas, A. S. & Ablowitz, M. J. 1982 On a unified approach to transformations and elementary solutions of Painlevé equations. J. Math. Phys. 23, 2033-2042.
    • (1982) J. Math. Phys. , vol.23 , pp. 2033-2042
    • Fokas, A.S.1    Ablowitz, M.J.2
  • 27
    • 0001465096 scopus 로고
    • On the inverse scattering transform of multidimensional nonlinear evolution equations related to first-order systems in the plane
    • Fokas, A. S. & Ablowitz, M. J. 1984 On the inverse scattering transform of multidimensional nonlinear evolution equations related to first-order systems in the plane. J. Math. Phys. 25, 2494-2505.
    • (1984) J. Math. Phys. , vol.25 , pp. 2494-2505
    • Fokas, A.S.1    Ablowitz, M.J.2
  • 28
    • 0001394512 scopus 로고
    • Coherent structures in multidimensions
    • Fokas, A. S. & Santini, P. M. 1989 Coherent structures in multidimensions. Phys. Rev. Lett. 63, 1329-1333.
    • (1989) Phys. Rev. Lett. , vol.63 , pp. 1329-1333
    • Fokas, A.S.1    Santini, P.M.2
  • 29
    • 4244193388 scopus 로고
    • Dromions and a boundary value problem for the Davey-Stewartson I equation
    • Fokas, A. S. & Santini, P. M. 1990 Dromions and a boundary value problem for the Davey-Stewartson I equation. Physica 44D, 99-130.
    • (1990) Physica , vol.44 D , pp. 99-130
    • Fokas, A.S.1    Santini, P.M.2
  • 30
    • 0009198444 scopus 로고
    • Lax pairs, Bäcklund transformations and special solutions for ordinary differential equations
    • Gibbon, J. D., Newell, A. C., Tabor, M. & Zeng, Y. B. 1988 Lax pairs, Bäcklund transformations and special solutions for ordinary differential equations. Nonlinearity 1, 481-490.
    • (1988) Nonlinearity , vol.1 , pp. 481-490
    • Gibbon, J.D.1    Newell, A.C.2    Tabor, M.3    Zeng, Y.B.4
  • 31
    • 0000662642 scopus 로고
    • Theory of Painlevé's equation
    • Gromak, V. I. 1975 Theory of Painlevé's equation. Diffl Equat. 11, 285-287.
    • (1975) Diffl Equat. , vol.11 , pp. 285-287
    • Gromak, V.I.1
  • 32
    • 0000071959 scopus 로고
    • One-parameter systems of solutions of Painlevé's equations
    • Gromak, V. I. 1977 One-parameter systems of solutions of Painlevé's equations. Diffl Equat. 14, 1510-1513.
    • (1977) Diffl Equat. , vol.14 , pp. 1510-1513
    • Gromak, V.I.1
  • 33
    • 0002247504 scopus 로고
    • Review of symbolic software for the computation of Lie symmetries of differential equations
    • Hereman, W. 1994 Review of symbolic software for the computation of Lie symmetries of differential equations. Euromath. Bull. 1(2), 45-79.
    • (1994) Euromath. Bull. , vol.1 , Issue.2 , pp. 45-79
    • Hereman, W.1
  • 35
    • 3142552246 scopus 로고
    • On moving pseudospherical surfaces: A generalised Weingarten system and its formal analysis
    • Johnson, M. E., Rogers, C., Schief, W. K. & Seiler, W. M. 1994 On moving pseudospherical surfaces: a generalised Weingarten system and its formal analysis. Lie Groups Applicat. 1, 124-136.
    • (1994) Lie Groups Applicat. , vol.1 , pp. 124-136
    • Johnson, M.E.1    Rogers, C.2    Schief, W.K.3    Seiler, W.M.4
  • 36
    • 84972507758 scopus 로고
    • Rational solutions of the fifth Painlevé equation
    • Kitaev, A. V., Law, C. K. & McLeod, J. B. 1994 Rational solutions of the fifth Painlevé equation. Diffl Int. Equat. 7, 967-1000.
    • (1994) Diffl Int. Equat. , vol.7 , pp. 967-1000
    • Kitaev, A.V.1    Law, C.K.2    McLeod, J.B.3
  • 37
    • 21144466740 scopus 로고
    • Similarity solutions of the deformed Maxwell-Bloch system
    • Kitaev, A. V., Rybin, A. V. & Timonen, J. 1993 Similarity solutions of the deformed Maxwell-Bloch system. J. Phys. A 26, 3583-3595.
    • (1993) J. Phys. A , vol.26 , pp. 3583-3595
    • Kitaev, A.V.1    Rybin, A.V.2    Timonen, J.3
  • 39
    • 0006245996 scopus 로고
    • The (2+1)-dimensional integrable generalization of the sine-Gordon equations. I. ∂-∂̄-dressing and the initial value problem
    • Konopelchenko, B. G. & Dubrovsky, V. G. 1993 The (2+1)-dimensional integrable generalization of the sine-Gordon equations. I. ∂-∂̄-dressing and the initial value problem. Stud. Appl. Math. 90, 189-223.
    • (1993) Stud. Appl. Math. , vol.90 , pp. 189-223
    • Konopelchenko, B.G.1    Dubrovsky, V.G.2
  • 40
    • 0000052719 scopus 로고
    • On 2 + 1-dimensional nonlinear systems of Loewner type
    • Konopelchenko, B. G. & Rogers, C. 1991 On 2 + 1-dimensional nonlinear systems of Loewner type. Phys. Lett. 158A, 391-397.
    • (1991) Phys. Lett. , vol.158 A , pp. 391-397
    • Konopelchenko, B.G.1    Rogers, C.2
  • 41
    • 33646819537 scopus 로고
    • On generalized Loewner systems: Novel integrable equations in 2 + 1-dimensional
    • Konopelchenko, B. G. & Rogers, C. 1993 On generalized Loewner systems: novel integrable equations in 2 + 1-dimensional. J. Math. Phys. 34, 214-242.
    • (1993) J. Math. Phys. , vol.34 , pp. 214-242
    • Konopelchenko, B.G.1    Rogers, C.2
  • 42
    • 0001945071 scopus 로고
    • A (2 + 1)-dimensional sine-Gordon system: Its auto-Bäcklund transformation
    • Konopelchenko, B. G., Schief, W. & Rogers, C. 1992 A (2 + 1)-dimensional sine-Gordon system: its auto-Bäcklund transformation. Phys. Lett. 172A 39-48.
    • (1992) Phys. Lett. , vol.172 A , pp. 39-48
    • Konopelchenko, B.G.1    Schief, W.2    Rogers, C.3
  • 43
    • 0001678923 scopus 로고
    • Nonclassical symmetry reduction: Example of the Boussinesq equation
    • Levi, D. & Winternitz, P. 1989 Nonclassical symmetry reduction: example of the Boussinesq equation. J. Phys. A 22, 2915-2924.
    • (1989) J. Phys. A , vol.22 , pp. 2915-2924
    • Levi, D.1    Winternitz, P.2
  • 44
    • 51249194887 scopus 로고
    • Generation of solutions of systems of partial differential equations by composition of infinitesimal Bäcklund transformations
    • Loewner, C. 1952 Generation of solutions of systems of partial differential equations by composition of infinitesimal Bäcklund transformations. J. Analyt. Math. 2, 219-242.
    • (1952) J. Analyt. Math. , vol.2 , pp. 219-242
    • Loewner, C.1
  • 45
    • 0002218551 scopus 로고
    • Elementary solutions of certain Painlevé equations
    • Lukashevich, N. A. 1965 Elementary solutions of certain Painlevé equations. Diffl Equat. 1, 561-564.
    • (1965) Diffl Equat. , vol.1 , pp. 561-564
    • Lukashevich, N.A.1
  • 47
    • 0342776711 scopus 로고
    • Applications of the differential algebra package diffgrob2 to reductions of PDE
    • (ed. W. F. Ames), Georgia Institute of Technology
    • Mansfield, E. L. & Clarkson, P. A. 1994 Applications of the differential algebra package diffgrob2 to reductions of PDE. In Proc. 14th IMACS World Congress on Computation and Applied Mathematics (ed. W. F. Ames), vol. 1, pp. 336-339. Georgia Institute of Technology
    • (1994) Proc. 14th IMACS World Congress on Computation and Applied Mathematics , vol.1 , pp. 336-339
    • Mansfield, E.L.1    Clarkson, P.A.2
  • 48
    • 85020825233 scopus 로고
    • Rational solutions and Bäcklund transformations for the third Painlevé equation
    • (ed. P. A. Clarkson), (NATO ASI Series C: Mathematical and Physical Sciences). Dordrecht: Kluwer
    • Milne, A. E. & Clarkson, P. A. 1993 Rational solutions and Bäcklund transformations for the third Painlevé equation. In Applications of analytic and geometric methods to nonlinear differential equations (ed. P. A. Clarkson), vol. 413, pp. 341-352 (NATO ASI Series C: Mathematical and Physical Sciences). Dordrecht: Kluwer.
    • (1993) Applications of Analytic and Geometric Methods to Nonlinear Differential Equations , vol.413 , pp. 341-352
    • Milne, A.E.1    Clarkson, P.A.2
  • 49
    • 0002101436 scopus 로고
    • Rational solutions of the second and fourth Painlevé equations
    • Murato, Y. 1985 Rational solutions of the second and fourth Painlevé equations. Funkcial. Ekvacioj 28, 1-32.
    • (1985) Funkcial. Ekvacioj , vol.28 , pp. 1-32
    • Murato, Y.1
  • 50
    • 0000594092 scopus 로고
    • A class of solutions of the Konopelchenko-Rogers equations
    • Nimmo, J. J. C. 1992 A class of solutions of the Konopelchenko-Rogers equations. Phys. Lett. 168A, 113-119.
    • (1992) Phys. Lett. , vol.168 A , pp. 113-119
    • Nimmo, J.J.C.1
  • 51
    • 0344181423 scopus 로고
    • Darboux transformations in (2+1)-dimensions
    • (ed. P. A. Clarkson), (NATO ASI Series C: Mathematical and Physical Sciences). Dordrecht: Kluwer
    • Nimmo, J. J. C. 1993 Darboux transformations in (2+1)-dimensions. In Applications of analytic and geometric methods to nonlinear differential equations (ed. P. A. Clarkson), vol. 413, pp. 183-192 (NATO ASI Series C: Mathematical and Physical Sciences). Dordrecht: Kluwer.
    • (1993) Applications of Analytic and Geometric Methods to Nonlinear Differential Equations , vol.413 , pp. 183-192
    • Nimmo, J.J.C.1
  • 54
    • 0002189586 scopus 로고
    • On gasdynamic-solitonic connections
    • (ed. P. A. Clarkson), (NATO ASI Series C: Mathematical and Physical Sciences). Dordrecht: Kluwer
    • Rogers, C. 1993 On gasdynamic-solitonic connections. In Applications of analytic and geometric methods to nonlinear differential equations (ed. P. A. Clarkson), vol. 413, pp. 217-228 (NATO ASI Series C: Mathematical and Physical Sciences). Dordrecht: Kluwer.
    • (1993) Applications of Analytic and Geometric Methods to Nonlinear Differential Equations , vol.413 , pp. 217-228
    • Rogers, C.1
  • 55
    • 21144471601 scopus 로고
    • On localized solitonic solutions of a (2+1)-dimensional sine-Gordon system
    • Schief, W. K. 1992 On localized solitonic solutions of a (2+1)-dimensional sine-Gordon system. J. Phys. A 25, L1351-L1354.
    • (1992) J. Phys. A , vol.25
    • Schief, W.K.1
  • 56
    • 21344490441 scopus 로고
    • Bäcklund transformations for the (un)pumped Maxwell-Bloch system and the fifth Painlevé equation
    • Schief, W. K. 1994 Bäcklund transformations for the (un)pumped Maxwell-Bloch system and the fifth Painlevé equation. J. Phys. A 27, 547-557.
    • (1994) J. Phys. A , vol.27 , pp. 547-557
    • Schief, W.K.1
  • 57
    • 36749112076 scopus 로고
    • The Painlevé property for partial differential equations
    • Weiss, J., Tabor, M. & Carnevale, G. 1983 The Painlevé property for partial differential equations. J. Math. Phys. 24, 522-526.
    • (1983) J. Math. Phys. , vol.24 , pp. 522-526
    • Weiss, J.1    Tabor, M.2    Carnevale, G.3
  • 59
    • 0342811366 scopus 로고
    • Physical applications of Painlevé type equations quadratic in the highest derivatives
    • (ed. P. Winternitz & D. Levi), (NATO ASI Series B: Physics). New York: Plenum
    • Winternitz, P. 1992 Physical applications of Painlevé type equations quadratic in the highest derivatives. In Painlevé transcendents, their asymptotics and physical applications (ed. P. Winternitz & D. Levi), vol. 278, pp. 425-431 (NATO ASI Series B: Physics). New York: Plenum.
    • (1992) Painlevé Transcendents, Their Asymptotics and Physical Applications , vol.278 , pp. 425-431
    • Winternitz, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.