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Remarks on nonlinear Schrdinger equations in one space dimension

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83290

Title: Remarks on nonlinear Schrdinger equations in one space dimension
Authors: Hayashi, Nakao Browse this author
Ozawa, Tohru Browse this author
Issue Date: Apr-1992
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 146
Start Page: 2
End Page: 10
Abstract: We consider the initial value problem for nonlinear Schodinger equations :{i8tu+ ½82u = F(u,8u,'ii,8'ii), (t,:z:) E ]R+ X IR, u(O,:z:)=uo(:z:), :z:EIR,}where 8 = 82 = 8/8:z:, F : C4 -+ C is a polynomial having no constant nor linear terms. Without smallness condition on the data uo, it is shown that (t) have a unique local solution in time if uo is in H3•0 n H2•1 , where Hm,• = {/ E S'; 11/llm,a = 11(1 + :z:2 )½(1- 􀀸)Zf' /ll2 < oo}, m,s E !R.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/68892
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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