메뉴 건너뛰기




Volumn 12, Issue 1, 2010, Pages 1-22

Bifurcation and secondary bifurcation of heavy periodic hydroelastic travelling waves

Author keywords

Bifurcation theory; Free boundary problems; Hydrodynamic waves; Hydroelastic waves; Lyapunov Schmidt reduction; Nonlinear elasticity; Secondary bifurcations; Symmetry breaking; Travelling waves; Wilton ripples

Indexed keywords


EID: 77955068691     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/224     Document Type: Article
Times cited : (14)

References (17)
  • 2
    • 0039234635 scopus 로고
    • Local and global aspects of the .1; n/mode interaction for capillary-gravity waves
    • Zbl 0737.76006 MR 1129004
    • ASTON, P. J. Local and global aspects of the .1;n/ mode interaction for capillary-gravity waves. Phys. D 52 (1991), 415-428. Zbl 0737.76006 MR 1129004.
    • (1991) Phys. D , vol.52 , pp. 415-428
    • Aston, P.J.1
  • 3
    • 38249002760 scopus 로고
    • Understanding the global solutions of the capillary-gravity wave problem
    • Zbl 0778.76010 MR 1209433
    • ASTON, P. J. Understanding the global solutions of the capillary-gravity wave problem. Wave Motion 17 (1993), 113-141. Zbl 0778.76010 MR 1209433.
    • (1993) Wave Motion , vol.17 , pp. 113-141
    • Aston, P.J.1
  • 4
    • 79953293427 scopus 로고    scopus 로고
    • Steady periodic water waves under nonlinear elastic membranes
    • to appear
    • BALDI, P., & TOLAND, J. F. Steady periodic water waves under nonlinear elastic membranes. J. Reine Angew. Math., to appear.
    • J. Reine Angew. Math.
    • Baldi, P.1    Toland, J.F.2
  • 5
    • 0003913603 scopus 로고
    • North-Holland Amsterdam
    • BOHR, N. Collected Works. North-Holland, Amsterdam (1906), pp. 67-78.
    • (1906) Collected Works , pp. 67-78
    • Bohr, N.1
  • 6
    • 0028410689 scopus 로고
    • Resonant capillary-gravity interfacial waves
    • Zbl 0806.76014 MR 1271683
    • CHRISTODOULIDES, P., & DIAS, F. Resonant capillary-gravity interfacial waves. J. Fluid Mech. 265 (1994), 303-343. Zbl 0806.76014 MR 1271683.
    • (1994) J. Fluid Mech. , vol.265 , pp. 303-343
    • Christodoulides, P.1    Dias, F.2
  • 7
    • 0042014763 scopus 로고    scopus 로고
    • Analytic description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping)
    • DYACHENKO, A. I., KUZNETSOV, E. A., SPECTOR, M. D., & ZAKHAROV, V. E. Analytic description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping). Phys. Lett. A 221 (1996), 73-79.
    • (1996) Phys. Lett. A , vol.221 , pp. 73-79
    • Dyachenko, A.I.1    Kuznetsov, E.A.2    Spector, M.D.3    Zakharov, V.E.4
  • 8
    • 0022904427 scopus 로고
    • Symmetry and the bifurcation of capillary-gravity waves
    • Zbl 0615.76023 MR 0853974
    • JONES, M. C. W., & TOLAND, J. F. Symmetry and the bifurcation of capillary-gravity waves. Arch. Ration. Mech. Anal. 96 (1986), 29-53. Zbl 0615.76023 MR 0853974.
    • (1986) Arch. Ration. Mech. Anal. , vol.96 , pp. 29-53
    • Jones, M.C.W.1    Toland, J.F.2
  • 9
    • 77955063123 scopus 로고    scopus 로고
    • Strain-gradient theory of hydroelastic travelling waves and their singular limits
    • in preparation
    • PLOTNIKOV, P. I., & TOLAND, J. F. Strain-gradient theory of hydroelastic travelling waves and their singular limits. Univ. of Bath, in preparation.
    • Univ. of Bath
    • Plotnikov, P.I.1    Toland, J.F.2
  • 10
    • 63449126043 scopus 로고    scopus 로고
    • Bernoulli free-boundary problems
    • Zbl 1167.35001 MR 2458311
    • SHARGORODSKY, E., & TOLAND, J. F. Bernoulli free-boundary problems. Mem. Amer. Math. Soc. 196, no.914 (2008). Zbl 1167.35001 MR 2458311.
    • (2008) Mem. Amer. Math. Soc. , vol.196 , Issue.914
    • Shargorodsky, E.1    Toland, J.F.2
  • 11
    • 36349013255 scopus 로고    scopus 로고
    • Heavy hydroelastic travelling waves
    • Zbl pre05229570 MR 2345232
    • TOLAND, J. F. Heavy hydroelastic travelling waves. Proc. R. Soc. Lond. A 463 (2007), 2371-2397. Zbl pre05229570 MR 2345232.
    • (2007) Proc. R. Soc. Lond. A , vol.463 , pp. 2371-2397
    • Toland, J.F.1
  • 12
    • 45049088237 scopus 로고    scopus 로고
    • Steady periodic hydroelastic waves
    • Zbl 1147.76008 MR 2413099
    • TOLAND, J. F. Steady periodic hydroelastic waves. Arch. Ration. Mech. Anal. 189 (2008), 325-362. Zbl 1147.76008 MR 2413099.
    • (2008) Arch. Ration. Mech. Anal. , vol.189 , pp. 325-362
    • Toland, J.F.1
  • 13
    • 24344505554 scopus 로고    scopus 로고
    • Riemann-Hilbert and variational structure for standing waves
    • Zbl pre02163182 MR 2108570
    • TOLAND, J. F., & IOOSS, G. Riemann-Hilbert and variational structure for standing waves. Far East J. Appl. Math. 15 (2004), 459-488. Zbl pre02163182 MR 2108570.
    • (2004) Far East J. Appl. Math. , vol.15 , pp. 459-488
    • Toland, J.F.1    Iooss, G.2
  • 14
    • 0022421262 scopus 로고
    • The bifurcation and secondary bifurcation of capillary-gravity waves
    • Zbl 0575.76023 MR 0799114
    • TOLAND, J. F., & JONES, M. C. W. The bifurcation and secondary bifurcation of capillary-gravity waves. Proc. R. Soc. Lond. A 399 (1985), 391-417. Zbl 0575.76023 MR 0799114.
    • (1985) Proc. R. Soc. Lond. A , vol.399 , pp. 391-417
    • Toland, J.F.1    Jones, M.C.W.2
  • 15
    • 0000334516 scopus 로고
    • On ripples
    • JFM 45.1090.02
    • WILTON, J. R. On ripples. Philos. Mag. (6) 29 (1915), 688-700. JFM 45.1090.02.
    • (1915) Philos. Mag. , vol.6 , Issue.29 , pp. 688-700
    • Wilton, J.R.1
  • 16
    • 34250447917 scopus 로고
    • Stability of periodic waves of finite amplitude on the surface of deep fluid
    • ZAKHAROV, V. E. Stability of periodic waves of finite amplitude on the surface of deep fluid. J. Appl. Mech. Tech. Phys. 2 (1968), 190-194.
    • (1968) J. Appl. Mech. Tech. Phys. , vol.2 , pp. 190-194
    • Zakharov, V.E.1
  • 17
    • 0003765696 scopus 로고    scopus 로고
    • Corrected reprint (1968) of 2nd ed., Cambridge Univ. Press, Cambridge, Zbl 0085.05601 MR 0107776
    • ZYGMUND, A. Trigonometric Series I & II. Corrected reprint (1968) of 2nd ed., Cambridge Univ. Press, Cambridge (1959). Zbl 0085.05601 MR 0107776
    • Trigonometric Series I & II , vol.1959
    • Zygmund, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.