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A Two-Soliton with Transient Turbulent Regime for the Cubic Half-Wave Equation on the Real Line

Gérard, Patrick and Lenzmann, Enno and Pocovnicu, Oana and Raphael, Pierre. (2018) A Two-Soliton with Transient Turbulent Regime for the Cubic Half-Wave Equation on the Real Line. Annals of PDE, 4 (7).

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Official URL: http://edoc.unibas.ch/58402/

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Abstract

We consider the focusing cubic half-wave equation on the real line
i∂tu+|D|u=|u|2u, |D|uˆ(ξ)=|ξ|u^(ξ), (t,x)∈R+×R.
We construct an asymptotic global-in-time compact two-soliton solution with arbitrarily small L2-norm which exhibits the following two regimes: (i) a transient turbulent regime characterized by a dramatic and explicit growth of its H1-norm on a finite time interval, followed by (ii) a saturation regime in which the H1-norm remains stationary large forever in time.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Lenzmann)
UniBasel Contributors:Lenzmann, Enno
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Springer
ISSN:2199-2576
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:30 Aug 2018 12:45
Deposited On:01 Jun 2018 09:25

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