Nonlinearity management in higher dimensions

Academic Article


  • In the present paper, we revisit nonlinearity management of the time-periodic nonlinear Schrödinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schrödinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H1 norm remains bounded, in contrast with the usual blow-up mechanism for the focusing Schrödinger equation. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management. © 2006 IOP Publishing Ltd.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Kevrekidis PG; Pelinovsky DE; Stefanov A
  • Start Page

  • 479
  • End Page

  • 488
  • Volume

  • 39
  • Issue

  • 3