On the new critical exponent for the nonlinear Schrödinger equations

Nakao Hayashi; Pavel I. Naumkin

doi:10.1007/s00030-013-0252-z

On the new critical exponent for the nonlinear Schrödinger equations

Nakao Hayashi, Pavel I. Naumkin

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

3 Citations (Scopus)

Abstract

We consider the Cauchy problem for the pth order nonlinear Schrödinger equation in one space dimension (Formula presented.) where (Formula presented.). We reveal that p = 4 is a new critical exponent with respect to the large time asymptotic behavior of solutions. We prove that if p_s < p < 4, then the large time asymptotics of solutions essentially differs from that for the linear case, whereas it has a quasilinear character for the case of p > 4.

Original language	English
Pages (from-to)	415-440
Number of pages	26
Journal	Nonlinear Differential Equations and Applications
Volume	21
Issue number	3
DOIs	https://doi.org/10.1007/s00030-013-0252-z
Publication status	Published - 2014 Jan
Externally published	Yes

Keywords

Asymptotics of solutions
New critical exponent
Nonlinear Schrödinger equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00030-013-0252-z

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abstract = "We consider the Cauchy problem for the pth order nonlinear Schr{\"o}dinger equation in one space dimension (Formula presented.) where (Formula presented.). We reveal that p = 4 is a new critical exponent with respect to the large time asymptotic behavior of solutions. We prove that if ps < p < 4, then the large time asymptotics of solutions essentially differs from that for the linear case, whereas it has a quasilinear character for the case of p > 4.",

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author = "Nakao Hayashi and Naumkin, {Pavel I.}",

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AU - Naumkin, Pavel I.

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N2 - We consider the Cauchy problem for the pth order nonlinear Schrödinger equation in one space dimension (Formula presented.) where (Formula presented.). We reveal that p = 4 is a new critical exponent with respect to the large time asymptotic behavior of solutions. We prove that if ps < p < 4, then the large time asymptotics of solutions essentially differs from that for the linear case, whereas it has a quasilinear character for the case of p > 4.

AB - We consider the Cauchy problem for the pth order nonlinear Schrödinger equation in one space dimension (Formula presented.) where (Formula presented.). We reveal that p = 4 is a new critical exponent with respect to the large time asymptotic behavior of solutions. We prove that if ps < p < 4, then the large time asymptotics of solutions essentially differs from that for the linear case, whereas it has a quasilinear character for the case of p > 4.

KW - Asymptotics of solutions

KW - New critical exponent

KW - Nonlinear Schrödinger equation

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JF - Nonlinear Differential Equations and Applications

SN - 1021-9722

IS - 3

ER -

On the new critical exponent for the nonlinear Schrödinger equations

Abstract

Keywords

ASJC Scopus subject areas

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