A quadratic nonlinear Schrödinger equation in one space dimension

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In this paper, we study the Cauchy problem for the quadratic derivative nonlinear Schrödinger equation {iut + UXX = (Ũx)2, (t, x) ε R2, {u(0, x) = u0, x ε R. We suppose that the initial data are small in the weighted Sobolev space H3,1(R) then we prove that there exist global in time small solutions to the Cauchy problem (*). We study the large time behavior of solutions and construct the modified asymptotics for large time values.

Original languageEnglish
Pages (from-to)165-185
Number of pages21
JournalJournal of Differential Equations
Issue number1
Publication statusPublished - 2002 Nov 20


  • Large time asymptotics
  • Nonlinear schrödinger equation


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