On the new critical exponent for the nonlinear Schrödinger equations

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We consider the Cauchy problem for the pth order nonlinear Schrödinger equation in one space dimension (Formula presented.) where (Formula presented.). We reveal that p = 4 is a new critical exponent with respect to the large time asymptotic behavior of solutions. We prove that if ps < p < 4, then the large time asymptotics of solutions essentially differs from that for the linear case, whereas it has a quasilinear character for the case of p > 4.

Original languageEnglish
Pages (from-to)415-440
Number of pages26
JournalNonlinear Differential Equations and Applications
Issue number3
Publication statusPublished - 2014 Jan


  • Asymptotics of solutions
  • New critical exponent
  • Nonlinear Schrödinger equation


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