Singular solutions of the subcritical nonlinear Schrödinger equation

Gadi Fibich

doi:10.1016/j.physd.2011.04.004

Singular solutions of the subcritical nonlinear Schrödinger equation

Gadi Fibich

School of Mathematical Sciences

Tel Aviv University

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

Abstract

We show that the subcritical d-dimensional nonlinear Schrdinger equation iψ_t+Δψ+| ψ |^2σψ=0, where 1<σd<2, admits smooth solutions that become singular in L ^p for p^*<p≤∞, where p ^*:=σd/σd-1. Since lim_σd→2- p^*=2, these solutions can collapse at any 2<p≤∞, and in particular for p=2σ+2.

Original language	English
Pages (from-to)	1119-1122
Number of pages	4
Journal	Physica D: Nonlinear Phenomena
Volume	240
Issue number	13
DOIs	https://doi.org/10.1016/j.physd.2011.04.004
State	Published - 15 Jul 2011

Keywords

Nonlinear Schrdinger equation
Singularity
Subcritical

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/j.physd.2011.04.004

Cite this

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title = "Singular solutions of the subcritical nonlinear Schr{\"o}dinger equation",

abstract = "We show that the subcritical d-dimensional nonlinear Schrdinger equation iψt+Δψ+| ψ |2σψ=0, where 1<σd<2, admits smooth solutions that become singular in L p for p**:=σd/σd-1. Since limσd→2- p*=2, these solutions can collapse at any 2",

keywords = "Nonlinear Schrdinger equation, Singularity, Subcritical",

author = "Gadi Fibich",

note = "Funding Information: This research was partially supported by the Israel Science Foundation (ISF grant No. 123/08 ).",

year = "2011",

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doi = "10.1016/j.physd.2011.04.004",

language = "الإنجليزيّة",

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N1 - Funding Information: This research was partially supported by the Israel Science Foundation (ISF grant No. 123/08 ).

PY - 2011/7/15

Y1 - 2011/7/15

N2 - We show that the subcritical d-dimensional nonlinear Schrdinger equation iψt+Δψ+| ψ |2σψ=0, where 1<σd<2, admits smooth solutions that become singular in L p for p**:=σd/σd-1. Since limσd→2- p*=2, these solutions can collapse at any 2

AB - We show that the subcritical d-dimensional nonlinear Schrdinger equation iψt+Δψ+| ψ |2σψ=0, where 1<σd<2, admits smooth solutions that become singular in L p for p**:=σd/σd-1. Since limσd→2- p*=2, these solutions can collapse at any 2

KW - Nonlinear Schrdinger equation

KW - Singularity

KW - Subcritical

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U2 - 10.1016/j.physd.2011.04.004

DO - 10.1016/j.physd.2011.04.004

M3 - مقالة

SN - 0167-2789

VL - 240

SP - 1119

EP - 1122

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 13

ER -

Singular solutions of the subcritical nonlinear Schrödinger equation

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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