142
Views
19
CrossRef citations to date
0
Altmetric
Original Articles

Bounds for the nonlinear Schrödinger approximation of the Fermi–Pasta–Ulam system

Pages 1523-1539 | Received 09 Jun 2009, Accepted 08 Aug 2009, Published online: 17 Feb 2010

References

  • Fermi , E , Pasta , J and Ulam , S . Studies of nonlinear problems, Tech. Rep. I., Los Alamos Rep, LA1940, Los Alamos, 1955 (Reproduced in Nonlinear Wave Motion, A.C. Newell, ed. AMS, Providence, RI, 1974)
  • Zabusky , NJ and Kruskal , MD . 1965 . Interactions of solitons in a collisionless plasma and the recurrence of initial states . Phys. Rev. Lett. , 15 : 240 – 243 .
  • Schneider , G and Wayne , CE . 2000 . “ Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi–Pasta–Ulam model ” . In Proceedings of Equadiff'99 , Edited by: Fiedler , B . Vol. 1 , 390 – 404 . Singapore : World Scientific .
  • Giannoulis , J and Mielke , A . 2004 . The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities . Nonlinearity , 17 ( 2 ) : 551 – 565 .
  • Giannoulis , J and Mielke , A . 2006 . Dispersive evolution of pulses in oscillator chains with general interaction potentials . Discr. Contin. Dyn. Syst.-Ser. B , 6 ( 3 ) : 493 – 523 .
  • Kirrmann , P , Schneider , G and Mielke , A . 1992 . The validity of modulation equations for extended systems with cubic nonlinearities . Proc. Roy. Soc. Edinburgh Sect. A , 122 ( 1–2 ) : 85 – 91 .
  • Kalyakin , LA . 1988 . Asymptotic decay of a one-dimensional wave packet in a nonlinear dispersive medium . Math. USSR Sbornik Surveys , 60 ( 2 ) : 457 – 483 .
  • Schneider , G . 1998 . Justification of modulation equations for hyperbolic systems via normal forms . NoDEA Nonlinear Diff. Eqns. Appl. , 5 ( 1 ) : 69 – 82 .
  • Düll , W-P and Schneider , G . 2006 . Justification of the nonlinear Schrödinger equation for a resonant Boussinesq model . Indiana Univ. Math. J. , 55 : 1813 – 1834 .
  • Schneider , G . 2005 . Justification and failure of the Nonlinear Schrödinger equation in case of non-trivial quadratic resonances . J. Diff. Eqns. , 216 : 354 – 386 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.