Remark on the global existence and large time asymptotics of solutions for the quadratic NLS

Nakao Hayashi, Pavel I. Naumkin

研究成果: Article査読

4 被引用数 (Scopus)

抄録

We study the global in time existence of small solutions to the nonlinear Schrödinger equation with quadratic interactions i ∂tu+12Δu=|u|2,t>0,x R4,u(0,x)= u0(x),x R4. We prove that if the initial data u0 satisfy smallness conditions in the weighted Sobolev norm, then the solution of the Cauchy problem (0.1) exists globally in time. Furthermore, we prove the existence of the usual scattering states and find the large time asymptotics of the solutions.

本文言語English
ページ(範囲)6950-6964
ページ数15
ジャーナルNonlinear Analysis, Theory, Methods and Applications
74
18
DOI
出版ステータスPublished - 2011 12
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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