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

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

JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)

ID	4165947
Author(s)	Gérard, Patrick; Lenzmann, Enno; Pocovnicu, Oana; Raphael, Pierre
Author(s) at UniBasel	Lenzmann, Enno
Year	2018
Title	A Two-Soliton with Transient Turbulent Regime for the Cubic Half-Wave Equation on the Real Line
Journal	Annals of PDE
Volume	4
Number	7
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.
Publisher	Springer
ISSN/ISBN	2199-2576
edoc-URL	http://edoc.unibas.ch/58402/
Full Text on edoc	No
Digital Object Identifier DOI	10.1007/s40818-017-0043-7

19/04/2024

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