Analyticity and global existence of small solutions to some nonlinear Schrödinger equations

Nakao Hayashi; Saburou Saitoh

doi:10.1007/BF02096777

Analyticity and global existence of small solutions to some nonlinear Schrödinger equations

Nakao Hayashi, Saburou Saitoh

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

36 Citations (Scopus)

Abstract

In this paper we will study the nonlinear Schrödinger equations: {Mathematical expression}. It is shown that the solutions of (*) exist and are analytic in space variables for t∈ℝ{set minus}{0} if φ(x) (∈H^{2 n+1,2}(ℝ_xⁿ)) decay exponentially as |x|→∞ and n≧2.

Original language	English
Pages (from-to)	27-41
Number of pages	15
Journal	Communications in Mathematical Physics
Volume	129
Issue number	1
DOIs	https://doi.org/10.1007/BF02096777
Publication status	Published - 1990 Apr
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02096777

Cite this

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title = "Analyticity and global existence of small solutions to some nonlinear Schr{\"o}dinger equations",

abstract = "In this paper we will study the nonlinear Schr{\"o}dinger equations: {Mathematical expression}. It is shown that the solutions of (*) exist and are analytic in space variables for t∈ℝ{set minus}{0} if φ(x) (∈H2 n+1,2(ℝxn)) decay exponentially as |x|→∞ and n≧2.",

author = "Nakao Hayashi and Saburou Saitoh",

year = "1990",

month = apr,

doi = "10.1007/BF02096777",

language = "English",

volume = "129",

pages = "27--41",

journal = "Communications in Mathematical Physics",

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AU - Saitoh, Saburou

PY - 1990/4

Y1 - 1990/4

N2 - In this paper we will study the nonlinear Schrödinger equations: {Mathematical expression}. It is shown that the solutions of (*) exist and are analytic in space variables for t∈ℝ{set minus}{0} if φ(x) (∈H2 n+1,2(ℝxn)) decay exponentially as |x|→∞ and n≧2.

AB - In this paper we will study the nonlinear Schrödinger equations: {Mathematical expression}. It is shown that the solutions of (*) exist and are analytic in space variables for t∈ℝ{set minus}{0} if φ(x) (∈H2 n+1,2(ℝxn)) decay exponentially as |x|→∞ and n≧2.

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U2 - 10.1007/BF02096777

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AN - SCOPUS:0007935383

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -

Analyticity and global existence of small solutions to some nonlinear Schrödinger equations

Abstract

ASJC Scopus subject areas

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