Differential and Integral Equations

On the existence of self-similar solutions of the nonlinear Schrödinger equation with power nonlinearity between 1 and 2

Giulia Furioli

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Abstract

We improve on a previous result by Ribaud and Youssfi on existence of self-similar solutions for the nonlinear Schrödinger equation, extending the range of available nonlinearities $\alpha +1 $ to $\alpha$ smaller than 1. We exploit the different behavior of the linear and nonlinear terms.

Article information

Source
Differential Integral Equations, Volume 14, Number 10 (2001), 1259-1266.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356123100

Mathematical Reviews number (MathSciNet)
MR1852461

Zentralblatt MATH identifier
1021.35102

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35A05 35K55: Nonlinear parabolic equations

Citation

Furioli, Giulia. On the existence of self-similar solutions of the nonlinear Schrödinger equation with power nonlinearity between 1 and 2. Differential Integral Equations 14 (2001), no. 10, 1259--1266. https://projecteuclid.org/euclid.die/1356123100


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