메뉴 건너뛰기




Volumn 206, Issue 1, 2007, Pages 251-277

The solution of the two-dimensional sine-Gordon equation using the method of lines

Author keywords

Finite difference method; Method of lines; Sine Gordon equation; Soliton

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; FINITE DIFFERENCE METHOD; INITIAL VALUE PROBLEMS; LINEAR STABILITY ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; SOLITONS;

EID: 34249277434     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.07.002     Document Type: Article
Times cited : (130)

References (38)
  • 1
    • 34249307652 scopus 로고    scopus 로고
    • M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Math. Soc. Lecture Note Ser. (1991) 149.
  • 2
  • 3
    • 0011755885 scopus 로고    scopus 로고
    • Exponentially tapered Josephson flux-flow oscillator
    • Benabdallah A., Caputo J.G., and Scott A.C. Exponentially tapered Josephson flux-flow oscillator. Phys. Rev. B 54 22 (1996) 16139-16146
    • (1996) Phys. Rev. B , vol.54 , Issue.22 , pp. 16139-16146
    • Benabdallah, A.1    Caputo, J.G.2    Scott, A.C.3
  • 4
    • 0347563209 scopus 로고
    • Oscillating particle-like solutions of the nonlinear Klein-Gordon equation
    • Bogolyubskiǐ I.L. Oscillating particle-like solutions of the nonlinear Klein-Gordon equation. JETP Lett. 24 10 (1976) 535-538
    • (1976) JETP Lett. , vol.24 , Issue.10 , pp. 535-538
    • Bogolyubskiǐ, I.L.1
  • 5
    • 0001217910 scopus 로고
    • Dynamics of spherically symmetrical pulsons of large amplitude
    • Bogolyubskiǐ I.L. Dynamics of spherically symmetrical pulsons of large amplitude. JETP Lett. 25 2 (1977) 107-110
    • (1977) JETP Lett. , vol.25 , Issue.2 , pp. 107-110
    • Bogolyubskiǐ, I.L.1
  • 6
    • 0002454698 scopus 로고
    • Lifetime of pulsating solitons in certain classical models
    • Bogolyubskiǐ I.L., and Makhankov V.G. Lifetime of pulsating solitons in certain classical models. JETP Lett. 24 1 (1976) 12-14
    • (1976) JETP Lett. , vol.24 , Issue.1 , pp. 12-14
    • Bogolyubskiǐ, I.L.1    Makhankov, V.G.2
  • 7
    • 33847382284 scopus 로고    scopus 로고
    • An explicit numerical scheme for the sine-Gordon equation in 2 + 1 dimensions
    • Bratsos A.G. An explicit numerical scheme for the sine-Gordon equation in 2 + 1 dimensions. Appl. Numer. Anal. Comput. Math. 2 2 (2005) 189-211
    • (2005) Appl. Numer. Anal. Comput. Math. , vol.2 , Issue.2 , pp. 189-211
    • Bratsos, A.G.1
  • 9
    • 0001329612 scopus 로고
    • Numerical solutions of 2 + 1 dimensional sine-Gordon solitons
    • Christiansen P.L., and Lomdahl P.S. Numerical solutions of 2 + 1 dimensional sine-Gordon solitons. Physica 2D (1981) 482-494
    • (1981) Physica , vol.2 D , pp. 482-494
    • Christiansen, P.L.1    Lomdahl, P.S.2
  • 10
    • 0039735415 scopus 로고
    • Return effect for rotationally symmetric solitary wave solutions to the sine-Gordon equation
    • Christiansen P.L., and Olsen O.H. Return effect for rotationally symmetric solitary wave solutions to the sine-Gordon equation. Phys. Lett. 68A 2 (1978) 185-188
    • (1978) Phys. Lett. , vol.68 A , Issue.2 , pp. 185-188
    • Christiansen, P.L.1    Olsen, O.H.2
  • 11
    • 0001713359 scopus 로고
    • On dynamical two-dimensional solutions to the sine-Gordon equation
    • Christiansen P.L., and Olsen O.H. On dynamical two-dimensional solutions to the sine-Gordon equation. Z. Angew. Math. Mech. 59 (1979) T30
    • (1979) Z. Angew. Math. Mech. , vol.59
    • Christiansen, P.L.1    Olsen, O.H.2
  • 12
    • 84908773326 scopus 로고
    • Ring-shaped quasi-soliton solutions to the two and three-dimensional sine-Gordon equations
    • Christiansen P.L., and Olsen O.H. Ring-shaped quasi-soliton solutions to the two and three-dimensional sine-Gordon equations. Phys. Scripta 20 (1979) 531-538
    • (1979) Phys. Scripta , vol.20 , pp. 531-538
    • Christiansen, P.L.1    Olsen, O.H.2
  • 13
    • 0029332275 scopus 로고
    • Numerical solutions of a damped sine-Gordon equation in two space variables
    • Djidjeli K., Price W.G., and Twizell E.H. Numerical solutions of a damped sine-Gordon equation in two space variables. J. Eng. Math. 29 (1995) 347-369
    • (1995) J. Eng. Math. , vol.29 , pp. 347-369
    • Djidjeli, K.1    Price, W.G.2    Twizell, E.H.3
  • 14
    • 0034229815 scopus 로고    scopus 로고
    • Curvature-induced symmetry breaking in nonlinear Schrödinger models
    • Gaididei Yu.B., Mingaleev S.F., and Christiansen P.L. Curvature-induced symmetry breaking in nonlinear Schrödinger models. Phys. Rev. E 62 1 (2000) R53-R56
    • (2000) Phys. Rev. E , vol.62 , Issue.1
    • Gaididei, Yu.B.1    Mingaleev, S.F.2    Christiansen, P.L.3
  • 15
    • 0004630711 scopus 로고
    • On the reflection of radially symmetrical sine-Gordon kinks in the origin
    • Geicke J. On the reflection of radially symmetrical sine-Gordon kinks in the origin. Phys. Lett. 98A 4 (1983) 147-150
    • (1983) Phys. Lett. , vol.98 A , Issue.4 , pp. 147-150
    • Geicke, J.1
  • 16
    • 84908814453 scopus 로고
    • Cylindrical pulsons in nonlinear relativistic wave equations
    • Geicke J. Cylindrical pulsons in nonlinear relativistic wave equations. Phys. Scripta 29 (1984) 431-434
    • (1984) Phys. Scripta , vol.29 , pp. 431-434
    • Geicke, J.1
  • 17
    • 33847355536 scopus 로고
    • The interaction of n-dimensional soliton wave fronts
    • Gibbon J.D., and Zambotti G. The interaction of n-dimensional soliton wave fronts. Nuovo Cimento 25B (1976) 1
    • (1976) Nuovo Cimento , vol.25 B , pp. 1
    • Gibbon, J.D.1    Zambotti, G.2
  • 18
    • 42749107019 scopus 로고    scopus 로고
    • C. Gorria, Yu.B. Gaididei, M.P. Soerensen, P.L. Christiansen, J.G. Caputo, Kink propagation and trapping in a two-dimensional curved Josephson junction, Phys. Rev. B 69 (2004) 134506 (1-10).
  • 19
    • 51249184038 scopus 로고
    • Special solution of the sine-Gordon equation in 2 + 1 dimensions
    • Grella G., and Marinaro M. Special solution of the sine-Gordon equation in 2 + 1 dimensions. Lett. Nuovo Cimento 23 (1978) 459
    • (1978) Lett. Nuovo Cimento , vol.23 , pp. 459
    • Grella, G.1    Marinaro, M.2
  • 21
    • 0000054867 scopus 로고    scopus 로고
    • Nonlinear whispering gallery modes
    • Harayama T., Davis P., and Ikeda K.S. Nonlinear whispering gallery modes. Phys. Rev. Lett. 82 19 (1999) 3803-3806
    • (1999) Phys. Rev. Lett. , vol.82 , Issue.19 , pp. 3803-3806
    • Harayama, T.1    Davis, P.2    Ikeda, K.S.3
  • 22
    • 56149120397 scopus 로고
    • Exact three-soliton solution of the two-dimensional sine-Gordon equation
    • Hirota R. Exact three-soliton solution of the two-dimensional sine-Gordon equation. J. Phys. Soc. Japan 35 (1973) 1566
    • (1973) J. Phys. Soc. Japan , vol.35 , pp. 1566
    • Hirota, R.1
  • 23
    • 0010502036 scopus 로고
    • Kadomtsev-Petviashvili and two-dimensional sine-Gordon equations: reduction to Painlevè transcendents
    • Kaliappan P., and Lakshmanan M. Kadomtsev-Petviashvili and two-dimensional sine-Gordon equations: reduction to Painlevè transcendents. J. Phys. A 12 (1979) L249
    • (1979) J. Phys. A , vol.12
    • Kaliappan, P.1    Lakshmanan, M.2
  • 24
    • 0040053372 scopus 로고
    • Exact solution of the n-dimensional sine-Gordon equation
    • Kobayashi K.K., and Izutsu M. Exact solution of the n-dimensional sine-Gordon equation. J. Phys. Soc. Japan 41 (1976) 1091
    • (1976) J. Phys. Soc. Japan , vol.41 , pp. 1091
    • Kobayashi, K.K.1    Izutsu, M.2
  • 25
    • 34249324318 scopus 로고
    • Transverse instability of breathers in resonant media
    • Kodama Y., and Ablowitz M.J. Transverse instability of breathers in resonant media. J. Math. Phys. 21 4 (1980) 928-931
    • (1980) J. Math. Phys. , vol.21 , Issue.4 , pp. 928-931
    • Kodama, Y.1    Ablowitz, M.J.2
  • 28
    • 0042839647 scopus 로고
    • New exact solutions of the classical sine-Gordon equation in 2 + 1 and 3 + 1 dimensions
    • Leibbrandt G. New exact solutions of the classical sine-Gordon equation in 2 + 1 and 3 + 1 dimensions. Phys. Rev. Lett. 41 (1978) 435-438
    • (1978) Phys. Rev. Lett. , vol.41 , pp. 435-438
    • Leibbrandt, G.1
  • 29
    • 45949131601 scopus 로고
    • Decay of shrinking solitons in multidimensional sine-Gordon equation
    • Malomed B.A. Decay of shrinking solitons in multidimensional sine-Gordon equation. Phys. D 24 (1987) 155-171
    • (1987) Phys. D , vol.24 , pp. 155-171
    • Malomed, B.A.1
  • 30
    • 0039863559 scopus 로고
    • Dynamic of quasi-one-dimensional kinks in the two-dimensional sine-Gordon model
    • Malomed B.A. Dynamic of quasi-one-dimensional kinks in the two-dimensional sine-Gordon model. Phys. D 52 (1991) 157-170
    • (1991) Phys. D , vol.52 , pp. 157-170
    • Malomed, B.A.1
  • 31
    • 0022053126 scopus 로고
    • Dynamics of rotationally symmetric solitons in near-SG field model with applications to large-area Josephson junctions and ferromagnets
    • Maslov E.M. Dynamics of rotationally symmetric solitons in near-SG field model with applications to large-area Josephson junctions and ferromagnets. Phys. D 15 (1985) 433-443
    • (1985) Phys. D , vol.15 , pp. 433-443
    • Maslov, E.M.1
  • 32
    • 0039692068 scopus 로고
    • Rotationally symmetric sG oscillator with tunable frequency
    • Maslov E.M. Rotationally symmetric sG oscillator with tunable frequency. Phys. Lett. A 131 6 (1988) 364-367
    • (1988) Phys. Lett. A , vol.131 , Issue.6 , pp. 364-367
    • Maslov, E.M.1
  • 33
    • 0034295749 scopus 로고    scopus 로고
    • Long-range interaction and nonlinear localized modes in photonic crystal waveguides
    • Mingaleev S.F., Kivshar Y.S., and Sammut R.A. Long-range interaction and nonlinear localized modes in photonic crystal waveguides. Phys. Rev. E 62 (2000) 5777-5782
    • (2000) Phys. Rev. E , vol.62 , pp. 5777-5782
    • Mingaleev, S.F.1    Kivshar, Y.S.2    Sammut, R.A.3
  • 34
    • 0016101698 scopus 로고
    • Numerical analysis of vortex motion on Josephson structures
    • Nakajima K., Onodera Y., Nakamura T., and Sato R. Numerical analysis of vortex motion on Josephson structures. J. Appl. Phys. 45 9 (1974) 4095-4099
    • (1974) J. Appl. Phys. , vol.45 , Issue.9 , pp. 4095-4099
    • Nakajima, K.1    Onodera, Y.2    Nakamura, T.3    Sato, R.4
  • 35
    • 18144406135 scopus 로고    scopus 로고
    • Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme
    • Sheng Q., Khaliq A.Q.M., and Voss D.A. Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme. Math. Comput. Simulation 68 (2005) 355-373
    • (2005) Math. Comput. Simulation , vol.68 , pp. 355-373
    • Sheng, Q.1    Khaliq, A.Q.M.2    Voss, D.A.3
  • 37
    • 0346688073 scopus 로고    scopus 로고
    • Modeling light bullets with the two-dimensional sine-Gordon equation
    • Xin J.X. Modeling light bullets with the two-dimensional sine-Gordon equation. Phys. D 135 (2000) 345-368
    • (2000) Phys. D , vol.135 , pp. 345-368
    • Xin, J.X.1
  • 38
    • 0010501637 scopus 로고
    • Particular solutions of the sine-Gordon equation in 2 + 1 dimensions
    • Zagrodzinsky J. Particular solutions of the sine-Gordon equation in 2 + 1 dimensions. Phys. Lett. 72A (1979) 284-286
    • (1979) Phys. Lett. , vol.72 A , pp. 284-286
    • Zagrodzinsky, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.