메뉴 건너뛰기




Volumn 125, Issue 3-4, 1999, Pages 201-221

Periodic and chaotic behaviour in a reduced form of the perturbed generalized Korteweg-de Vries and Kadomtsev-Petviashvili equations

Author keywords

Chaotic behaviour; Kadomtsev Petviashvili equation; Korteweg de Vries equation; Melnikov function; Perturbation system

Indexed keywords


EID: 0000171084     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00242-5     Document Type: Article
Times cited : (19)

References (35)
  • 2
    • 0020916122 scopus 로고
    • Three-dimensional nonlinear long waves due to moving surface pressure
    • Ann Arbor, Mich.
    • D.-M. Wu, T.Y. Wu, Three-dimensional nonlinear long waves due to moving surface pressure, in: Proceedings of the 14th Symposium on Nav. Hydrodyn. Ann Arbor, Mich., 1982, pp. 103-129.
    • (1982) Proceedings of the 14th Symposium on Nav. Hydrodyn. , pp. 103-129
    • Wu, D.-M.1    Wu, T.Y.2
  • 3
    • 0021406188 scopus 로고
    • On the excitation of long nonlinear water waves by a moving pressure distribution
    • T.R. Akylas, On the excitation of long nonlinear water waves by a moving pressure distribution, J. Fluid Mech. 141 (1984) 455-466.
    • (1984) J. Fluid Mech. , vol.141 , pp. 455-466
    • Akylas, T.R.1
  • 4
    • 0022161461 scopus 로고
    • Transient waves produced by flow past a bump
    • S.L. Cole, Transient waves produced by flow past a bump, Wave motion 7 (1985) 579-587.
    • (1985) Wave Motion , vol.7 , pp. 579-587
    • Cole, S.L.1
  • 5
    • 0024610432 scopus 로고
    • Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances
    • S.J. Lee, G.T. Gates, T.Y. Wu, Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances, J. Fluid Mech. 199 (1989) 569-593.
    • (1989) J. Fluid Mech. , vol.199 , pp. 569-593
    • Lee, S.J.1    Gates, G.T.2    Wu, T.Y.3
  • 6
    • 0022441988 scopus 로고
    • Resonant flow of a stratified fluid over topography
    • R.H.J. Grimshaw, N. Smyth, Resonant flow of a stratified fluid over topography, J. Fluid Mech. 169 (1986) 429-464.
    • (1986) J. Fluid Mech. , vol.169 , pp. 429-464
    • Grimshaw, R.H.J.1    Smyth, N.2
  • 7
    • 0023147301 scopus 로고
    • On the excitation of long nonlinear water waves by a moving pressure distribution. Part 2. Three-dimensional effects
    • C. Katsis, T.R. Akylas, On the excitation of long nonlinear water waves by a moving pressure distribution. Part 2. Three-dimensional effects, J. Fluid Mech. 177 (1987) 49-65.
    • (1987) J. Fluid Mech. , vol.177 , pp. 49-65
    • Katsis, C.1    Akylas, T.R.2
  • 9
    • 0028384852 scopus 로고
    • On the three-dimensional internal waves excited by topography in the flow of a stratified fluid
    • H. Hanazaki, On the three-dimensional internal waves excited by topography in the flow of a stratified fluid, J. Fluid Mech. 263 (1994) 293-318.
    • (1994) J. Fluid Mech. , vol.263 , pp. 293-318
    • Hanazaki, H.1
  • 10
    • 0023717524 scopus 로고
    • Dissipation effects on the resonant flow of a stratified fluid over topography
    • N.F. Smyth, Dissipation effects on the resonant flow of a stratified fluid over topography, J. Fluid Mech. 192 (1988) 287-312.
    • (1988) J. Fluid Mech. , vol.192 , pp. 287-312
    • Smyth, N.F.1
  • 11
    • 0023348446 scopus 로고
    • Transcritical two-layer flow over topography
    • W.K. Melville, K.R. Helfrich, Transcritical two-layer flow over topography, J. Fluid Mech. 178 (1987) 31-52.
    • (1987) J. Fluid Mech. , vol.178 , pp. 31-52
    • Melville, W.K.1    Helfrich, K.R.2
  • 12
    • 0028768192 scopus 로고
    • Periodic and chaotic behaviour in a reduction of the perturbed Korteweg-de Vries equation
    • Series A
    • R.H.J. Grimshaw, X. Tian, Periodic and chaotic behaviour in a reduction of the perturbed Korteweg-de Vries equation, Proc. R. Soc. London, Series A 445 (1994) 1-21.
    • (1994) Proc. R. Soc. London , vol.445 , pp. 1-21
    • Grimshaw, R.H.J.1    Tian, X.2
  • 13
    • 0017901962 scopus 로고
    • A numerical and theoretical study of certain nonlinear wave phenomena
    • Series A
    • B. Fomberg, G.B. Whitham, A numerical and theoretical study of certain nonlinear wave phenomena, Phil. Trans. R. Soc. London, Series A 289 (1978) 373-404.
    • (1978) Phil. Trans. R. Soc. London , vol.289 , pp. 373-404
    • Fomberg, B.1    Whitham, G.B.2
  • 14
    • 8744250514 scopus 로고    scopus 로고
    • Remarks on the generalized Kadomtsev-Petviashvili equations and two-dimensional Benjamin-Ono equations
    • Series A
    • G. Boling, H. Yongqian, Remarks on the generalized Kadomtsev-Petviashvili equations and two-dimensional Benjamin-Ono equations, Proc. R. Soc. London, Series A 452 (1996) 1585-1595.
    • (1996) Proc. R. Soc. London , vol.452 , pp. 1585-1595
    • Boling, G.1    Yongqian, H.2
  • 15
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular channel, and a new type of long stationary wave
    • D.J. Korteweg, G. de Vries, On the change of form of long waves advancing in a rectangular channel, and a new type of long stationary wave, Phil. Mag. Ser. 5(39) (1895) 422-443.
    • (1895) Phil. Mag. Ser. , vol.5 , Issue.39 , pp. 422-443
    • Korteweg, D.J.1    De Vries, G.2
  • 16
    • 0000262859 scopus 로고
    • On the stability of solitary waves in weakly dispersing media
    • B.B. Kadomtsev, V.I. Petviashvili, On the stability of solitary waves in weakly dispersing media, Soviet Phys. Doklady, 15 (1970) 539-541.
    • (1970) Soviet Phys. Doklady , vol.15 , pp. 539-541
    • Kadomtsev, B.B.1    Petviashvili, V.I.2
  • 17
    • 0020507454 scopus 로고
    • A second-order theory for solitary waves in shallow fluids
    • J.A. Gear, R. Grimshaw, A second-order theory for solitary waves in shallow fluids, Phys. Fluids 26 (1983) 14-29.
    • (1983) Phys. Fluids , vol.26 , pp. 14-29
    • Gear, J.A.1    Grimshaw, R.2
  • 18
    • 0000177219 scopus 로고
    • Homoclinic crossings and pattern selection
    • H.T. Moon, Homoclinic crossings and pattern selection, Phys. Rev. Lett. 64 (1990) 412-414.
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 412-414
    • Moon, H.T.1
  • 19
    • 2942611338 scopus 로고
    • Soliton turbulence and strange attractor
    • H.T. Moon, Soliton turbulence and strange attractor, Phys. Fluid A 3 (1991) 2709-2715.
    • (1991) Phys. Fluid A , vol.3 , pp. 2709-2715
    • Moon, H.T.1
  • 20
    • 0344279801 scopus 로고
    • Periodic doubling in a perturbed sine-Gordon system
    • D.J. Zheng, W.J. Yeh, O.G. Symko, Periodic doubling in a perturbed sine-Gordon system, Phys. Lett. 179 (1989) 225-228.
    • (1989) Phys. Lett. , vol.179 , pp. 225-228
    • Zheng, D.J.1    Yeh, W.J.2    Symko, O.G.3
  • 21
    • 0002389545 scopus 로고
    • Dynamical chaos of solitons and nonlinear periodic waves
    • F.Kh. Abdullaev, Dynamical chaos of solitons and nonlinear periodic waves, Phys. Rep. 179 (1989) 1-78.
    • (1989) Phys. Rep. , vol.179 , pp. 1-78
    • Abdullaev, F.Kh.1
  • 22
    • 0022476053 scopus 로고
    • The evolution of resonant water-wave oscillations
    • E. Cox, M.P. Mortell, The evolution of resonant water-wave oscillations, J. Fluid Mech. 162 (1986) 99-116.
    • (1986) J. Fluid Mech. , vol.162 , pp. 99-116
    • Cox, E.1    Mortell, M.P.2
  • 23
    • 0001482143 scopus 로고
    • The local-global analysis of the simulated Brillouin scattering in the regime of nonlinear sound waves
    • W. Rozmus, M. Casanova, D. Pesme, A. Heron, J.C. Adam, The local-global analysis of the simulated Brillouin scattering in the regime of nonlinear sound waves, Phys. Fluids B 4 (1992) 576-593.
    • (1992) Phys. Fluids B , vol.4 , pp. 576-593
    • Rozmus, W.1    Casanova, M.2    Pesme, D.3    Heron, A.4    Adam, J.C.5
  • 24
    • 0001697223 scopus 로고
    • Chaotic phenomena triggering the escape from a potential well
    • Series A
    • J.M.T. Thompson, Chaotic phenomena triggering the escape from a potential well, Proc. R. Soc. London, Series A 421 (1989) 195-225.
    • (1989) Proc. R. Soc. London , vol.421 , pp. 195-225
    • Thompson, J.M.T.1
  • 25
    • 45149144707 scopus 로고
    • Intermittencies and power-law low frequency divergencies in a nonlinear oscillator
    • M.A. Rubio, M. De La Torre, J.C. Antoranz, Intermittencies and power-law low frequency divergencies in a nonlinear oscillator, Physica D 36 (1989) 92-108.
    • (1989) Physica D , vol.36 , pp. 92-108
    • Rubio, M.A.1    De La Torre, M.2    Antoranz, J.C.3
  • 26
    • 0027927383 scopus 로고
    • Dynamic analysis of ship capsizing in regular waves
    • I. Senjanovic, Y. Fan, Dynamic analysis of ship capsizing in regular waves, Brodogradnja 42 (1994) 51-60.
    • (1994) Brodogradnja , vol.42 , pp. 51-60
    • Senjanovic, I.1    Fan, Y.2
  • 29
    • 8744265566 scopus 로고
    • Extended results of subharmonic resonance bifurcation of a class of nonlinear Mathieu equations
    • Stuttgart, Germany, Springer, Berlin
    • Y. Chen, K. Zhan, W.F. Langford, Extended results of subharmonic resonance bifurcation of a class of nonlinear Mathieu equations, in: Nonlinear Dynamics in Engineering Systems IUTAM Symposium, Stuttgart, Germany, Springer, Berlin, 1989.
    • (1989) Nonlinear Dynamics in Engineering Systems IUTAM Symposium
    • Chen, Y.1    Zhan, K.2    Langford, W.F.3
  • 30
    • 0001834849 scopus 로고
    • On the stability of the centre for time period perturbation
    • V.K. Melnikov, On the stability of the centre for time period perturbation, Trans. Moscow Math. Soc. 12 (1963) 1-57.
    • (1963) Trans. Moscow Math. Soc. , vol.12 , pp. 1-57
    • Melnikov, V.K.1
  • 31
    • 85025784004 scopus 로고
    • An example of bifurcation to homoclinic orbits
    • S.N. Chow, J.K. Hale, J. Mallet-Paret, An example of bifurcation to homoclinic orbits, J. Diff. Eq. 37 (1980) 351-373.
    • (1980) J. Diff. Eq. , vol.37 , pp. 351-373
    • Chow, S.N.1    Hale, J.K.2    Mallet-Paret, J.3
  • 32
    • 0001991757 scopus 로고
    • Homoclinic orbits, subharmonic and global bifurcation in forced oscillation
    • G. Barenblatt, G. Iooss, D.D. Joseph (Eds.), Pitman, London
    • B.D. Greenspan, P.J. Holmes, Homoclinic orbits, subharmonic and global bifurcation in forced oscillation, in: G. Barenblatt, G. Iooss, D.D. Joseph (Eds.), Nonlinear Dynamics and Turbulence, Pitman, London, 1982.
    • (1982) Nonlinear Dynamics and Turbulence
    • Greenspan, B.D.1    Holmes, P.J.2
  • 35
    • 0008494528 scopus 로고
    • Determining Lyapunov exponents from a time series
    • A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Determining Lyapunov exponents from a time series, Physica D 16 (1985) 285-317.
    • (1985) Physica D , vol.16 , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.