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- W2558232744 abstract "We consider the focusing cubic half-wave equation on the real line $$begin{aligned} i partial _t u + |D| u = |u|^2 u, widehat{|D|u}(xi )=|xi |hat{u}(xi ), (t,x)in {mathbb {R}}_+times {mathbb {R}}. end{aligned}$$ We construct an asymptotic global-in-time compact two-soliton solution with arbitrarily small $$L^2$$ -norm which exhibits the following two regimes: (i) a transient turbulent regime characterized by a dramatic and explicit growth of its $$H^1$$ -norm on a finite time interval, followed by (ii) a saturation regime in which the $$H^1$$ -norm remains stationary large forever in time." @default.
- W2558232744 created "2016-12-08" @default.
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- W2558232744 date "2018-01-17" @default.
- W2558232744 modified "2023-10-15" @default.
- W2558232744 title "A Two-Soliton with Transient Turbulent Regime for the Cubic Half-Wave Equation on the Real Line" @default.
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- W2558232744 doi "https://doi.org/10.1007/s40818-017-0043-7" @default.
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