메뉴 건너뛰기




Volumn 8, Issue 3, 2009, Pages 909-930

Modulated and localized states in a finite domain*

Author keywords

Bifurcation; Homoclinic snaking; Pattern formation

Indexed keywords

AMPLITUDE-MODULATED; BIFURCATION; CRITICAL VALUE; CROSSLINKS; DIRICHLET; DOMAIN SIZE; FINITE DOMAINS; HOMOCLINIC SNAKING; INFINITE DOMAINS; LOCALIZED STATE; MODE INTERACTIONS; MODULATED STATE; NEUMANN BOUNDARY CONDITION; PATTERN FORMATION; PATTERN-FORMING INSTABILITY; PERIODIC BOUNDARY CONDITIONS; PERIODIC PATTERN; PERIODIC SOLUTION; PRIMARY INSTABILITY; QUINTIC NONLINEARITY; SADDLE NODE BIFURCATION; SWIFT-HOHENBERG EQUATIONS; WAVE NUMBERS;

EID: 68649095203     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/080724344     Document Type: Article
Times cited : (35)

References (38)
  • 1
    • 33744510968 scopus 로고    scopus 로고
    • Dissipative solitons
    • N. Akhmediev, A.Ankiewicz eds., Springer, Berlin
    • N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons, Lecture Notes in Phys. 661, Springer, Berlin, 2005.
    • (2005) Lecture Notes in Phys. , vol.661
  • 2
    • 21244506743 scopus 로고    scopus 로고
    • 4He mixtures in moderate aspect ratio containers
    • 4He mixtures in moderate aspect ratio containers, Phys. Fluids, 17 (2005), paper 064102.
    • (2005) Phys. Fluids , vol.17 , pp. 064102
    • Batiste, O.1    Knobloch, E.2
  • 8
    • 33751251449 scopus 로고    scopus 로고
    • Asymptotics of cellular buckling close to the Maxwell load
    • C. J. Budd, G. W. Hunt, and R. Kuske, Asymptotics of cellular buckling close to the Maxwell load, Proc. Roy. Soc. London, 457 (2001), pp. 2935-2964.
    • (2001) Proc. Roy. Soc. London , vol.457 , pp. 2935-2964
    • Budd, C.J.1    Hunt, G.W.2    Kuske, R.3
  • 9
    • 68649103196 scopus 로고    scopus 로고
    • Ph.D. thesis, Department of Physics, University of California at Berkeley, Berkeley, CA
    • J. Burke, Localized States in Driven Dissipative Systems, Ph.D. thesis, Department of Physics, University of California at Berkeley, Berkeley, CA, 2008.
    • (2008) Localized States in Driven Dissipative Systems
    • Burke, J.1
  • 11
    • 33744829750 scopus 로고    scopus 로고
    • Localized states in the generalized Swift-Hohenberg equation
    • J. Burke and E. Knobloch, Localized states in the generalized Swift-Hohenberg equation, Phys. Rev. E, 73 (2006), paper 056211.
    • (2006) Phys. Rev. E , vol.73 , pp. 056211
    • Burke, J.1    Knobloch, E.2
  • 12
    • 33751252789 scopus 로고    scopus 로고
    • Snakes and ladders: Localized states in the Swift-Hohenberg equation
    • J. Burke and E. Knobloch, Snakes and ladders: Localized states in the Swift-Hohenberg equation, Phys. Lett. A, 360 (2007), pp. 681-688.
    • (2007) Phys. Lett. A , vol.360 , pp. 681-688
    • Burke, J.1    Knobloch, E.2
  • 13
    • 58149488792 scopus 로고    scopus 로고
    • Exponential asymptotics of localized patterns and snaking bifurcation diagrams
    • S. J. Chapman and G. Kozyreff, Exponential asymptotics of localized patterns and snaking bifurcation diagrams, Phys. D, 238 (2009), pp. 319-354.
    • (2009) Phys. D , vol.238 , pp. 319-354
    • Chapman, S.J.1    Kozyreff, G.2
  • 14
    • 0000841505 scopus 로고    scopus 로고
    • Stable static localized structures in one dimension
    • P. Coullet, C. Riera, and C. Tresser, Stable static localized structures in one dimension, Phys. Rev. Lett., 84 (2000), pp. 3069-3072.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 3069-3072
    • Coullet, P.1    Riera, C.2    Tresser, C.3
  • 15
    • 33846027126 scopus 로고    scopus 로고
    • Localized states in thermal convection with an imposed vertical magnetic field
    • J. H. P. Dawes, Localized states in thermal convection with an imposed vertical magnetic field, J. Fluid Mech., 570 (2007), pp. 385-406.
    • (2007) J. Fluid Mech. , vol.570 , pp. 385-406
    • Dawes, J.H.P.1
  • 16
    • 43049104801 scopus 로고    scopus 로고
    • Localized pattern formation with a large-scale mode: Slanted snaking
    • J. H. P. Dawes, Localized pattern formation with a large-scale mode: Slanted snaking, SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 186-206.
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , pp. 186-206
    • Dawes, J.H.P.1
  • 18
    • 0003270066 scopus 로고
    • Singularities and Groups in Bifurcation Theory
    • Springer, New York
    • M. Golubitsky, I. N. Stewart, and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol.II, Appl. Math. Sci. 69, Springer, New York, 1988.
    • (1988) Appl. Math. Sci. , vol.2 , pp. 69
    • Golubitsky, M.1    Stewart, I.N.2    Schaeffer, D.G.3
  • 19
    • 15944428231 scopus 로고    scopus 로고
    • Rigorous numerics for localized patterns to the quintic Swift-Hohenberg equation
    • Y. Hiraoka and T. Ogawa, Rigorous numerics for localized patterns to the quintic Swift-Hohenberg equation, Japan J. Indust. Appl. Math., 22 (2005), pp. 57-75.
    • (2005) Japan J. Indust. Appl. Math. , vol.22 , pp. 57-75
    • Hiraoka, Y.1    Ogawa, T.2
  • 20
    • 69949152747 scopus 로고    scopus 로고
    • Homoclinic snaking in bounded domains
    • to appear
    • S. M. Houghton and E. Knobloch, Homoclinic snaking in bounded domains, Phys. Rev. E, to appear.
    • Phys. Rev. E
    • Houghton, S.M.1    Knobloch, E.2
  • 22
    • 43949176143 scopus 로고
    • Periodic homoclinic solutions in reversible 1 : 1 resonance vector fields
    • G. Iooss and M.-C. Perouème, Periodic homoclinic solutions in reversible 1 : 1 resonance vector fields, J. Differential Equations, 102 (1993), pp. 62-88.
    • (1993) J. Differential Equations , vol.102 , pp. 62-88
    • Iooss, G.1    Perouème, M.-C.2
  • 23
    • 41549156504 scopus 로고    scopus 로고
    • Spatially localized structures in dissipative systems: Open problems
    • E. Knobloch, Spatially localized structures in dissipative systems: Open problems, Nonlinearity, 21 (2008), pp. T45-T60.
    • (2008) Nonlinearity , vol.21
    • Knobloch, E.1
  • 24
    • 33746376262 scopus 로고    scopus 로고
    • Asymptotics of large bound states of localized structures
    • G. Kozyreff and S. J. Chapman, Asymptotics of large bound states of localized structures, Phys. Rev. Lett., 97 (2006), paper 044502.
    • (2006) Phys. Rev. Lett. , vol.97 , pp. 044502
    • Kozyreff, G.1    Chapman, S.J.2
  • 26
    • 65249131771 scopus 로고    scopus 로고
    • Localized radial solutions of the Swift-Hohenberg equation
    • D. Lloyd and B. Sandstede, Localized radial solutions of the Swift-Hohenberg equation, Nonlinearity, 22 (2009), pp. 485-524.
    • (2009) Nonlinearity , vol.22 , pp. 485-524
    • Lloyd, D.1    Sandstede, B.2
  • 29
    • 11744373488 scopus 로고
    • Front motion, metastability and subcritical bifurcations in hydrodynamics
    • Y. Pomeau, Front motion, metastability and subcritical bifurcations in hydrodynamics, Phys. D, 23 (1986), pp. 3-11.
    • (1986) Phys. D , Issue.23 , pp. 3-11
    • Pomeau, Y.1
  • 30
    • 34248583204 scopus 로고    scopus 로고
    • Computing absolute and essential spectra using continuation
    • J. D. M. Rademacher, B. Sandstede, and A. Scheel, Computing absolute and essential spectra using continuation, Phys. D, 229 (2007), pp. 166-183.
    • (2007) Phys. D , Issue.229 , pp. 166-183
    • Rademacher, J.D.M.1    Sandstede, B.2    Scheel, A.3
  • 31
    • 27144464510 scopus 로고    scopus 로고
    • Two-dimensional solitons in the surface of magnetic fluids
    • R. Richter and I. V. Barashenkov, Two-dimensional solitons in the surface of magnetic fluids, Phys. Rev. Lett., 94 (2005), paper 184503.
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 184503
    • Richter, R.1    Barashenkov, I.V.2
  • 32
    • 0000204546 scopus 로고    scopus 로고
    • Localized structures in pattern-forming systems
    • M. Golubitsky, D. Luss, and S. H. Strogatz, eds., Springer, New York
    • H. Riecke, Localized structures in pattern-forming systems, in Pattern Formation in Continuous and Coupled Systems: A Survey Volume, IMA Vol. Math. Appl. 115, M. Golubitsky, D. Luss, and S. H. Strogatz, eds., Springer, New York, 1999, pp. 215-229.
    • (1999) Pattern Formation in Continuous and Coupled Systems: A Survey Volume, IMA Math. Appl. , vol.115 , pp. 215-229
    • Riecke, H.1
  • 33
    • 0001091641 scopus 로고    scopus 로고
    • Localization of waves without bistability: Worms in nematic electroconvection
    • H. Riecke and G. D. Granzow, Localization of waves without bistability: Worms in nematic electroconvection, Phys. Rev. Lett., 81 (1999), pp. 333-336.
    • (1999) Phys. Rev. Lett. , vol.81 , pp. 333-336
    • Riecke, H.1    Granzow, G.D.2
  • 34
    • 0000837163 scopus 로고    scopus 로고
    • Stable localized solutions of arbitrary length for the quintic Swift- Hohenberg equation
    • H. Sakaguchi and H. R. Brand, Stable localized solutions of arbitrary length for the quintic Swift- Hohenberg equation, Phys. D, 97 (1996), pp. 274-285.
    • (1996) Phys. D , Issue.97 , pp. 274-285
    • Sakaguchi, H.1    Brand, H.R.2
  • 35
    • 4243995835 scopus 로고    scopus 로고
    • Spatiotemporal filamentary patterns in a dc-driven planar gas discharge system
    • C. Strümple;, H.-G. Purwins, and Y. A. Astrov, Spatiotemporal filamentary patterns in a dc-driven planar gas discharge system, Phys. Rev. E, 63 (2001), paper 026409.
    • (2001) Phys. Rev. E , vol.63 , pp. 026409
    • Strümpel, C.1    Purwins, H.-G.2    Astrov, Y.A.3
  • 36
    • 0002773290 scopus 로고
    • Bifurcation analysis of the Eckhaus instability
    • L. S. Tuckerman and D. Barkley, Bifurcation analysis of the Eckhaus instability, Phys. D, 46 (1990), pp. 57-86.
    • (1990) Phys. D , Issue.46 , pp. 57-86
    • Tuckerman, L.S.1    Barkley, D.2
  • 37
    • 41349084544 scopus 로고    scopus 로고
    • Two-dimensional clusters of solitary structures in driven optical cavities
    • A. G. Vladimirov, J. M. McSloy, D. V. Skryabin, and W. J. Firth, Two-dimensional clusters of solitary structures in driven optical cavities, Phys. Rev. E, 65 (2002), paper 046606.
    • (2002) Phys. Rev. E , vol.65 , pp. 046606
    • Vladimirov, A.G.1    McSloy, J.M.2    Skryabin, D.V.3    Firth, W.J.4
  • 38
    • 0346500773 scopus 로고    scopus 로고
    • Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
    • P. D. Woods and A. R. Champneys, Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation, Phys. D, 129 (1999), pp. 147-170.
    • (1999) Phys. D , Issue.129 , pp. 147-170
    • Woods, P.D.1    Champneys, A.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.