Advances in Differential Equations

Stability and instability of traveling solitonic bubbles

Zhiwu Lin

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We study the nonlinear Schrödinger equation with general nonlinearity of competing type. This equation has traveling waves solution with non-vanishing condition at infinity in one dimension. We give a sharp condition for the stability and instability of these solutions. This justifies the previous prediction posed in physical literature.

Article information

Adv. Differential Equations, Volume 7, Number 8 (2002), 897-918.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B35: Stability


Lin, Zhiwu. Stability and instability of traveling solitonic bubbles. Adv. Differential Equations 7 (2002), no. 8, 897--918.

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