Remarks on nonlinear Schrödinger equations in one space dimension

Nakao Hayashi; Tohru Ozawa; J. L. Bona

Remarks on nonlinear Schrödinger equations in one space dimension

Nakao Hayashi, Tohru Ozawa, J. L. Bona

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂_x = ∂/∂x and F: C⁴ → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u₀, it is shown that (+) has a unique local solution in time if u₀ is in H^{3, 0} ∩ H^{2, 1}, where H^{m, s} = {f ∈ S’ ∥f∥^{m, s} = ∥(1 + x²)^s/2 (1-Δ)f∥

Original language	English
Pages (from-to)	453-461
Number of pages	9
Journal	Differential and Integral Equations
Volume	7
Issue number	2
Publication status	Published - 1994
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

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title = "Remarks on nonlinear Schr{\"o}dinger equations in one space dimension",

abstract = "We consider the initial value problem for nonlinear Sch{\"o}dinger equations, where ∂ = ∂x = ∂/∂x and F: C4 → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u0, it is shown that (+) has a unique local solution in time if u0 is in H3, 0 ∩ H2, 1, where Hm, s = {f ∈ S{\textquoteright} ∥f∥m, s = ∥(1 + x2)s/2 (1-Δ)f∥",

author = "Nakao Hayashi and Tohru Ozawa and Bona, {J. L.}",

year = "1994",

language = "English",

volume = "7",

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journal = "Differential and Integral Equations",

issn = "0893-4983",

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AU - Hayashi, Nakao

AU - Ozawa, Tohru

AU - Bona, J. L.

PY - 1994

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AB - We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂x = ∂/∂x and F: C4 → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u0, it is shown that (+) has a unique local solution in time if u0 is in H3, 0 ∩ H2, 1, where Hm, s = {f ∈ S’ ∥f∥m, s = ∥(1 + x2)s/2 (1-Δ)f∥

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ER -

Remarks on nonlinear Schrödinger equations in one space dimension

Abstract

ASJC Scopus subject areas

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