On the Barashenkov-Bogdan-Zhanlav solitons and their stability

Wen Feng, Milena Stanislavova and Atanas G. Stefanov

Chaos, Solitons & Fractals, 2021, vol. 152, issue C

Abstract: The Barashenkov-Bogdan-Zhanlav solitons u± for the forced NLS/Lugiato-Lefever model on the line are considered. While the instability of u+ was established in the original paper, [3], the analogous question for u− was only considered heuristically and numerically. We rigorously analyze the stability of u− in the various regime of the parameters. In particular, we show that u− is spectrally stable for small pump strength h. Moreover, u− remains spectrally stable until a pair of neutral eigenvalues of negative Krein signature hits another pair of eigenvalues, which has emanated from the edge of the continuous spectrum, [1,2,3]. After the collision, an instability is conjectured and numerically observed in previous works, [3].

Keywords: Solitons; Stability; Lugiato-Lefever model (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921008213

DOI: 10.1016/j.chaos.2021.111467

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