KAM for Reversible Derivative Wave Equations
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  • 作者:Massimiliano Berti (1) (2)
    Luca Biasco (3)
    Michela Procesi (4)
  • 刊名:Archive for Rational Mechanics and Analysis
  • 出版年:2014
  • 出版时间:June 2014
  • 年:2014
  • 卷:212
  • 期:3
  • 页码:905-955
  • 全文大小:655 KB
  • 参考文献:1. Arnold, V.I.: / Reversible Systems, Nonlinear and Turbulent Processes in Physics, vol. 3 (Kiev, 1983), pp. 1161鈥?174. Harwood Academic Publ., Chur, (1984)
    2. Berti M., Biasco L.: Branching of Cantor manifolds of elliptic tori and applications to PDEs. Commun. Math. Phys. 305(3), 741鈥?96 (2011) CrossRef
    3. Berti M., Biasco L., Procesi M.: KAM theory for the Hamiltonian derivative wave equation. Annales scientifique de l鈥橢NS 46(2): 301鈥?73 (2013)
    4. Berti M., Biasco L., Procesi M.: Existence and stability of quasi-periodic solutions of reversible derivative wave equations. Rend. Lincei Mat. Appl. 24, 1鈥?6 (2013)
    5. Berti M., Bolle P.: Sobolev quasi periodic solutions of multidimensional wave equations with a multiplicative potential. Nonlinearity 25, 2579鈥?613 (2012) CrossRef
    6. Biasco L., Di Gregorio L.: A Birkhoff-Lewis type theorem for the nonlinear wave equation. Arch. Ration. Mech. Anal. 196(1): 303鈥?62 (2010) CrossRef
    7. Bourgain, J.: Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. / Int. Math. Res. Notices 11 (1994)
    8. Bourgain, J.: Periodic solutions of nonlinear wave equations, Harmonic analysis and partial differential equations, Chicago Lectures in Mathematics, pp. 69鈥?7. Univ. Chicago Press, Chicago, (1999)
    9. Chierchia L., You J.: KAM tori for 1D nonlinear wave equations with periodic boundary conditions. Commun. Math. Phys. 211, 497鈥?25 (2000) CrossRef
    10. Craig, W.: Probl猫mes de petits diviseurs dans les 茅quations aux d茅riv茅es partielles, Panoramas et Synth猫ses, vol. 9. Soci茅t茅 Math茅matique de France, Paris, (2000)
    11. Craig, W., Wayne, C. E.: Newton鈥檚 method and periodic solutions of nonlinear wave equation. / Commun. Pure Appl. Math. 46, 1409鈥?498 (1993)
    12. Eliasson L.H., Kuksin S.: On reducibility of Schr枚dinger equations with quasiperiodic in time potentials. Commun. Math. Phys. 286, 125鈥?35 (2009) CrossRef
    13. Eliasson L.H., Kuksin S.: KAM for non-linear Schr枚dinger equation. Ann. Math. 172, 371鈥?35 (2010) CrossRef
    14. Gr茅bert, B., Thomann, L.: KAM for the quantum harmonic oscillator. / Commun. Math. Phys. 307(2), 383鈥?27 (2011)
    15. Liu J., Yuan X.: A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations. Commun. Math. Phys 307(3): 629鈥?73 (2011) CrossRef
    16. Kappeler, T., P枚schel, J.: / KAM and KdV. Springer, Berlin, (2003)
    17. Klainermann S., Majda A.: Formation of singularities for wave equations including the nonlinear vibrating string. Commun. Pure Appl. Math. 33, 241鈥?63 (1980) CrossRef
    18. Kuksin S.: A KAM theorem for equations of the Korteweg-de Vries type. Rev. Math. Math. Phys. 10(3): 1鈥?4 (1998)
    19. Kuksin, S.: / Analysis of Hamiltonian PDEs, Oxford Lecture Series in Mathematics and its Applications, vol. 19. Oxford University Press, Oxford, (2000)
    20. Moser, J.: Convergent series expansions for quasi-periodic motions. / Math. Ann. 169, 136鈥?76 (1967)
    21. P枚schel J.: Quasi-periodic solutions for a nonlinear wave equation. Comment. Math. Helv. 71(2): 269鈥?96 (1996) CrossRef
    22. Procesi, C., Procesi, M.: / A KAM algorithm for the completely resonant nonlinear Schr枚dinger equation (2012, preprint)
    23. Procesi M., Xu X.: Quasi-T枚plitz functions in KAM theorem. SIAM J. Math. Anal. 45(4): 2148鈥?181 (2013) CrossRef
    24. Rabinowitz, P.: Periodic solutions of nonlinear hyperbolic partial differential equations. / Commun. Pure Appl. Math. 20, 145鈥?05 (1967)
    25. Rabinowitz P.: Periodic solutions of nonlinear hyperbolic partial differential equations II. Commun. Pure Appl. Math. 22, 15鈥?9 (1968) CrossRef
    26. Sevryuk, M.B.: / Reversible Systems, Lecture Notes in Math, vol. 1211. Springer, Berlin, (1986)
    27. Wayne E.: Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory. Commun. Math. Phys. 127, 479鈥?28 (1990) CrossRef
    28. Zhang J., Gao M., Yuan X.: KAM tori for reversible partial differential equations. Nonlinearity 24, 1189鈥?228 (2011) CrossRef
  • 作者单位:Massimiliano Berti (1) (2)
    Luca Biasco (3)
    Michela Procesi (4)

    1. Dipartimento di Matematica e Applicazioni 鈥淩. Caccioppoli鈥? Universit脿 degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, 80126, Naples, Italy
    2. SISSA, Via Bonomea 265, 34136, Trieste, Italy
    3. Dipartimento di Matematica e Fisica, Universit脿 鈥淩oma Tre鈥? Largo S. L. Murialdo 1, 00146, Rome, Italy
    4. Dipartimento di Matematica 鈥淕. Castelnuovo鈥? Universit脿 degli Studi di Roma la Sapienza, P.le A. Moro 5, 00185, Rome, Italy
  • ISSN:1432-0673
文摘
We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

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