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Volumn 455, Issue 1986, 1999, Pages 2351-2370

Effects of exponentially small terms in the perturbation approach to localized buckling

Author keywords

Boundary value solutions; Elastic instability; Exponential asymptotics; Multimodal solutions; Solitary wave phenomena; Strut buckling

Indexed keywords


EID: 0008474556     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0407     Document Type: Article
Times cited : (23)

References (26)
  • 1
    • 21844524190 scopus 로고
    • On short-scale oscillatory tails of long-wave disturbances
    • Akylas, T. R. & Yang, T.-S. 1995 On short-scale oscillatory tails of long-wave disturbances. Stud. Appl. Math. 94, 1-20.
    • (1995) Stud. Appl. Math. , vol.94 , pp. 1-20
    • Akylas, T.R.1    Yang, T.-S.2
  • 2
    • 0002360911 scopus 로고
    • Uniform asymptotic smoothing of Stokes's discontinuities
    • Berry, M. V. 1989 Uniform asymptotic smoothing of Stokes's discontinuities. Proc. R. Soc. Land. A 422, 7-21.
    • (1989) Proc. R. Soc. Land. A , vol.422 , pp. 7-21
    • Berry, M.V.1
  • 3
    • 0010957727 scopus 로고
    • A hyperasymptotic perturbative method for computing the radiation coefficient for weakly nonlocal solitary waves
    • Boyd, J. P. 1995 A hyperasymptotic perturbative method for computing the radiation coefficient for weakly nonlocal solitary waves. J. Comp. Phys. 120, 15-32.
    • (1995) J. Comp. Phys. , vol.120 , pp. 15-32
    • Boyd, J.P.1
  • 4
    • 0030096092 scopus 로고    scopus 로고
    • Numerical computations of a nearly singular nonlinear equation: Weakly nonlocal bound states of solitons for the fifth-order Korteweg-de Vries equation
    • Boyd, J. P. 1996 Numerical computations of a nearly singular nonlinear equation: weakly nonlocal bound states of solitons for the fifth-order Korteweg-de Vries equation. J. Comp. Phys. 124, 55-70.
    • (1996) J. Comp. Phys. , vol.124 , pp. 55-70
    • Boyd, J.P.1
  • 5
    • 33746447114 scopus 로고    scopus 로고
    • Weakly nonlocal solitary waves and beyond-all-orders asymptotics
    • Boyd, J. P. 1998 Weakly nonlocal solitary waves and beyond-all-orders asymptotics. Dordrecht: Klmver.
    • (1998) Dordrecht: Klmver.
    • Boyd, J.P.1
  • 6
    • 53349120754 scopus 로고    scopus 로고
    • Bifurcation and coalescence of a plethora of multi-modal homoclinic orbits for a Hamiltonian system
    • Buffbni, B., Champneys, A. R. & Toland, J. F. 1997 Bifurcation and coalescence of a plethora of multi-modal homoclinic orbits for a Hamiltonian system. J. Dyn. Diff. Eqns 8, 221-281.
    • (1997) J. Dyn. Diff. Eqns , vol.8 , pp. 221-281
    • Buffbni, B.1    Champneys, A.R.2    Toland, J.F.3
  • 7
    • 21844508998 scopus 로고
    • Subsidiary homoclinic orbits to a saddle-focus for reversible systems
    • Champneys, A. R. 1994 Subsidiary homoclinic orbits to a saddle-focus for reversible systems. Int. Jl Bifurcation Chaos 4, 1447-1482.
    • (1994) Int. Jl Bifurcation Chaos , vol.4 , pp. 1447-1482
    • Champneys, A.R.1
  • 8
    • 36149031023 scopus 로고
    • Bifurcation of a plethora of multimodal homoclinic orbits for Hamiltonian systems
    • Champneys, A. R. & Toland, J. F. 1993 Bifurcation of a plethora of multimodal homoclinic orbits for Hamiltonian systems. Nonlinearity 6, 665-721.
    • (1993) Nonlinearity , vol.6 , pp. 665-721
    • Champneys, A.R.1    Toland, J.F.2
  • 9
    • 3142589149 scopus 로고    scopus 로고
    • Localization and solitary waves in solid mechanics
    • Champneys, A. R., Hunt, G. W. & Thompson, J. M. T.' (eds)
    • Champneys, A. R., Hunt, G. W. & Thompson, J. M. T.' (eds) 1997 Localization and solitary waves in solid mechanics. Phil. Trans. R. Soc. Land. A 355, 2073-2213.
    • (1997) Phil. Trans. R. Soc. Land. A , vol.355 , pp. 2073-2213
  • 11
    • 21344476611 scopus 로고
    • A note on the interaction between solitary waves in a singularly perturbed Korteweg-deVries equation
    • Grimshaw, R. & Malomed, B. A. 1993 A note on the interaction between solitary waves in a singularly perturbed Korteweg-deVries equation. J. Phys. A 26, 4087-4091.
    • (1993) J. Phys. A , vol.26 , pp. 4087-4091
    • Grimshaw, R.1    Malomed, B.A.2
  • 12
    • 0000925235 scopus 로고
    • Comparative Lagrangian formulations for localized buckling
    • Hunt, G. W. & Wadee, M. K. 1991 Comparative Lagrangian formulations for localized buckling. Proc. R. Soc. Lond. A 434, 485-502.
    • (1991) Proc. R. Soc. Lond. A , vol.434 , pp. 485-502
    • Hunt, G.W.1    Wadee, M.K.2
  • 13
    • 0007859149 scopus 로고
    • Structural localization phenomena and the dynamical phase-space analogy
    • Hunt, G. W., Bolt, H. M. & Thompson, J. M. T. 1989 Structural localization phenomena and the dynamical phase-space analogy. Proc. R. Soc. Land. A 425, 245-267.
    • (1989) Proc. R. Soc. Land. A , vol.425 , pp. 245-267
    • Hunt, G.W.1    Bolt, H.M.2    Thompson, J.M.T.3
  • 14
    • 0027867483 scopus 로고
    • Localized elasticac for the strut on the linear foundation
    • Hunt, G. W., Wadee, M. K. & Shiacolas, N. 1993 Localized elasticac for the strut on the linear foundation. ASME Jl Appl. Mech. 60, 1033-1038.
    • (1993) ASME Jl Appl. Mech. , vol.60 , pp. 1033-1038
    • Hunt, G.W.1    Wadee, M.K.2    Shiacolas, N.3
  • 15
    • 0032647267 scopus 로고    scopus 로고
    • Homoclinic and heteroclinic orbits under-lying the post-buckling of axially compressed cylindrical shells
    • Hunt, G. W., Lord, G. J. & Champneys, A. R. 1999 Homoclinic and heteroclinic orbits under-lying the post-buckling of axially compressed cylindrical shells. Comp. Meth. Appl. Mech. Engng 170, 239-251.
    • (1999) Comp. Meth. Appl. Mech. Engng , vol.170 , pp. 239-251
    • Hunt, G.W.1    Lord, G.J.2    Champneys, A.R.3
  • 16
    • 0014662728 scopus 로고
    • Finite bandwidth, finite amplitude convection
    • Newell, A. C. & Whitehead, J. A. 1969 Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38, 279-303.
    • (1969) J. Fluid Mech. , vol.38 , pp. 279-303
    • Newell, A.C.1    Whitehead, J.A.2
  • 17
    • 0002486903 scopus 로고
    • Stokes' phenomenon demystified
    • Paris, R. B. & Wood, A. D. 1995 Stokes' phenomenon demystified. IMA Bull. 31, 21-28.
    • (1995) IMA Bull. , vol.31 , pp. 21-28
    • Paris, R.B.1    Wood, A.D.2
  • 18
    • 0020862906 scopus 로고
    • Amplitude modulation, phase modulation and localization of buckling patterns
    • ed. J. M. T. Thompson & G. W. Hunt, pp. 149-159. Cambridge University Press.
    • Potier-Ferry, M. 1983 Amplitude modulation, phase modulation and localization of buckling patterns. In Collapse: the buckling of structures in theory and practice (ed. J. M. T. Thompson & G. W. Hunt), pp. 149-159. Cambridge University Press.
    • (1983) In Collapse: the Buckling of Structures in Theory and Practice
    • Potier-Ferry, M.1
  • 19
    • 3142624970 scopus 로고    scopus 로고
    • Instability of localized buckling modes in a one-dimensional strut model
    • Sandstede, B. 1997 Instability of localized buckling modes in a one-dimensional strut model. Phil. Trans. R. Soc. Land. A 355, 2083-2097.
    • (1997) Phil. Trans. R. Soc. Land. A , vol.355 , pp. 2083-2097
    • Sandstede, B.1
  • 20
    • 84959644006 scopus 로고
    • A nonlinear instability theory for a wave system in plane convection
    • Stewartson, K. & Stuart, J. T. 1971 A nonlinear instability theory for a wave system in plane convection. J. Fluid Mech. 48, 529-545.
    • (1971) J. Fluid Mech. , vol.48 , pp. 529-545
    • Stewartson, K.1    Stuart, J.T.2
  • 22
    • 0019065124 scopus 로고
    • On the localization of buckle patterns
    • Tvergaard, V. &: Needleman, A. 1980 On the localization of buckle patterns. J. Appl. Mech. 21, 613-619.
    • (1980) J. Appl. Mech. , vol.21 , pp. 613-619
    • Tvergaard, V.1    Needleman, A.2
  • 23
    • 0001665109 scopus 로고    scopus 로고
    • Asymptotic and Rayleigh-Ritz routes to localized buckling solutions in an elastic instability problem
    • Wadee, M. K., Hunt, G. W. & Whiting, A. I. M. 1997 Asymptotic and Rayleigh-Ritz routes to localized buckling solutions in an elastic instability problem. Proc. R. Soc. Land. A 453, 2085-2107.
    • (1997) Proc. R. Soc. Land. A , vol.453 , pp. 2085-2107
    • Wadee, M.K.1    Hunt, G.W.2    Whiting, A.I.M.3
  • 24
    • 85020785058 scopus 로고
    • MATHEMATICA: A system for doing mathematics by computer, v. 2.2
    • Wolfram Research Inc. 1995 MATHEMATICA: a system for doing mathematics by computer, v. 2.2. Champaign, IL: Wolfram Research, Inc.
    • (1995) Champaign, IL: Wolfram Research, Inc.
    • Inc, W.R.1
  • 25
    • 0346500773 scopus 로고    scopus 로고
    • Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian Hopf bifurcation
    • Woods, P. D. & Champneys, A. R. 1999 Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian Hopf bifurcation. Physica D129, 147-170.
    • (1999) Physica D , vol.129 , pp. 147-170
    • Champneys, A.R.1
  • 26
    • 0030769574 scopus 로고    scopus 로고
    • On asymmetric gravity-capillary solitary waves
    • Yang, T.-S. & Akylas, T. R. 1997 On asymmetric gravity-capillary solitary waves. J. Fluid Mech. 330, 215-232.
    • (1997) J. Fluid Mech. , vol.330 , pp. 215-232
    • Yang, T.-S.1    Akylas, T.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.