메뉴 건너뛰기




Volumn 13, Issue 3, 2005, Pages 541-552

Quasi-periodic solutions for completely resonant non-linear wave equations in ID and 2D

Author keywords

Infinite dimensional Hamiltonian Systems; Lyapunov Schmidt reduction; Nonlinear Wave Equation; Quasi periodic solutions

Indexed keywords


EID: 23844533735     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2005.13.541     Document Type: Article
Times cited : (16)

References (22)
  • 1
    • 0035541517 scopus 로고    scopus 로고
    • Normal form and exponential stability for some nonlinear string equations
    • D. Bambusi, S. Cacciatori, S. Paleari, Normal form and exponential stability for some nonlinear string equations, Z. Angew. Math. Phys. 52 (2001), no. 6, 1033-1052.
    • (2001) Z. Angew. Math. Phys. , vol.52 , Issue.6 , pp. 1033-1052
    • Bambusi, D.1    Cacciatori, S.2    Paleari, S.3
  • 2
    • 0002663649 scopus 로고    scopus 로고
    • Families of periodic solutions of resonant PDE's
    • D. Bambusi, S. Paleari, Families of periodic solutions of resonant PDE's, J. Nonlinear Sci. 11 (2001), no. 1, 69-87
    • (2001) J. Nonlinear Sci. , vol.11 , Issue.1 , pp. 69-87
    • Bambusi, D.1    Paleari, S.2
  • 3
    • 0345734391 scopus 로고    scopus 로고
    • Periodic solutions of nonlinear wave equations with general nonlinearities
    • M. Berti, P. Bolle, Periodic solutions of nonlinear wave equations with general nonlinearities, Comm. Math. Phys. 243 (2003), no. 2, 315-328.
    • (2003) Comm. Math. Phys. , vol.243 , Issue.2 , pp. 315-328
    • Berti, M.1    Bolle, P.2
  • 4
    • 0742307263 scopus 로고    scopus 로고
    • Multiplicity of periodic solutions of nonlinear wave equations
    • M. Berti, P. Bolle, Multiplicity of periodic solutions of nonlinear wave equations, Nonlinear Anal., no. 56 (2004), 1011-1046
    • (2004) Nonlinear Anal. , Issue.56 , pp. 1011-1046
    • Berti, M.1    Bolle, P.2
  • 6
    • 84963026889 scopus 로고
    • Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE
    • 475ff., approx. (electronic)
    • J. Bourgain, Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE, Internat. Math. Res. Notices 1994, no. 11, 475ff., approx. 21 pp. (electronic).
    • (1994) Internat. Math. Res. Notices , Issue.11
    • Bourgain, J.1
  • 7
    • 34249756262 scopus 로고
    • Construction of periodic solutions of nonlinear wave equations in higher dimension
    • J. Bourgain, Construction of periodic solutions of nonlinear wave equations in higher dimension, Geom. Funct. Anal. 5 (1995), 629-639.
    • (1995) Geom. Funct. Anal. , vol.5 , pp. 629-639
    • Bourgain, J.1
  • 8
    • 0032272850 scopus 로고    scopus 로고
    • Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
    • J. Bourgain, Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations, Ann. of Math. (2) 148 (1998), no. 2, 363-439.
    • (1998) Ann. of Math. (2) , vol.148 , Issue.2 , pp. 363-439
    • Bourgain, J.1
  • 9
    • 0034349017 scopus 로고    scopus 로고
    • KAM tori for 1D nonlinear wave equations with periodic boundary conditions
    • L.Chierchia, J. You, KAM tori for 1D nonlinear wave equations with periodic boundary conditions, Comm. Math. Phys. 211 (2) 2000 pp. 497-525
    • (2000) Comm. Math. Phys. , vol.211 , Issue.2 , pp. 497-525
    • Chierchia, L.1    You, J.2
  • 10
    • 8744221061 scopus 로고    scopus 로고
    • Problèmes de petits diviseurs dans les équations aux dérivées partielles
    • Société Mathématique de France, Paris
    • W. Craig, Problèmes de petits diviseurs dans les équations aux dérivées partielles, Panoramas and Syntheses 9. Société Mathématique de France, Paris, 2000.
    • (2000) Panoramas and Syntheses , vol.9
    • Craig, W.1
  • 11
    • 84990576596 scopus 로고
    • Newton's method and periodic solutions of nonlinear wave equations
    • W. Craig, E. Wayne, Newton's method and periodic solutions of nonlinear wave equations, Comm. Pure Appl. Math. 46 (1993), 1409-1498.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 1409-1498
    • Craig, W.1    Wayne, E.2
  • 12
    • 4344709451 scopus 로고    scopus 로고
    • Construction of periodic solutions of the nonlinear wave equation with Dirichlet boundary conditions by the Linsdtedt series method
    • to appear in
    • G. Gentile, V. Mastropietro, Construction of periodic solutions of the nonlinear wave equation with Dirichlet boundary conditions by the Linsdtedt series method, to appear in J. Math. Pures Appl. (9)
    • J. Math. Pures Appl. , Issue.9
    • Gentile, G.1    Mastropietro, V.2
  • 13
    • 17744365990 scopus 로고    scopus 로고
    • Periodic solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions
    • to appear in
    • G. Gentile, V. Mastropietro, M. Procesi Periodic solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions to appear in Comm. Math. Phys
    • Comm. Math. Phys
    • Gentile, G.1    Mastropietro, V.2    Procesi, M.3
  • 15
    • 0001836195 scopus 로고
    • Nearly integrable infinite-dimensional Hamiltonian systems
    • Springer, Berlin
    • S.B. Kuksin, Nearly integrable infinite-dimensional Hamiltonian systems, Lecture Notes in Mathematics 1556, Springer, Berlin, 1994.
    • (1994) Lecture Notes in Mathematics , vol.1556
    • Kuksin, S.B.1
  • 17
    • 0040157758 scopus 로고    scopus 로고
    • Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
    • S.B. Kuksin, J.Pöschel, Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation, Ann. of Math. (2) 143 (1996), no. 1, 149-179.
    • (1996) Ann. of Math. (2) , vol.143 , Issue.1 , pp. 149-179
    • Kuksin, S.B.1    Pöschel, J.2
  • 19
    • 0030443654 scopus 로고    scopus 로고
    • Quasi-periodic solutions for a nonlinear wave equation
    • J. Pöschel, Quasi-periodic solutions for a nonlinear wave equation, Comment. Math. Helv. 71 (1996), no. 2, 269-296.
    • (1996) Comment. Math. Helv. , vol.71 , Issue.2 , pp. 269-296
    • Pöschel, J.1
  • 21
    • 0000502263 scopus 로고
    • Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
    • C.E. Wayne, Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory, Comm. Math. Phys. 127 (1990), no. 3, 479-528.
    • (1990) Comm. Math. Phys. , vol.127 , Issue.3 , pp. 479-528
    • Wayne, C.E.1
  • 22
    • 0001459972 scopus 로고
    • Normal modes for nonlinear Hamiltonian systems
    • A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math. 20 (1973), 47-57.
    • (1973) Invent. Math. , vol.20 , pp. 47-57
    • Weinstein, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.