Asymptotic stability for spectrally stable Lugiato-Lefever solitons in periodic waveguides
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DOI: 10.1063/1.5048017
Abstract: We consider the Lugiato-Lefever model of optical fibers in the periodic context. Spectrally stable periodic steady states were constructed recently in the studies of Delcey and Haragus [Philos. Trans. R. Soc., A 376, 20170188 (2018)];… read more here.
Keywords: lugiato lefever; asymptotic stability; spectrally stable; steady states ... See more keywords
Construction of a spectrally stable self-similar blowup solution to the supercritical corotational harmonic map heat flow
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DOI: 10.1088/1361-6544/aabe4c
Abstract: We prove the existence of a (spectrally) stable self-similar blow-up solution $f_0$ to the heat flow for corotational harmonic maps from $\mathbb R^3$ to the three-sphere. In particular, our result verifies the spectral gap conjecture… read more here.
Keywords: heat flow; self similar; self; solution ... See more keywords
Euler-type relative equilibria in spaces of constant curvature and their stability
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DOI: 10.4153/cjm-2017-002-7
Abstract: We consider three point positive masses moving on S and H. An Eulerianrelative equilibrium, is a relative equilibriumwhere the threemasses are on the same geodesic, in this paper we analyze the spectral stability of these… read more here.
Keywords: case; relative equilibria; euler type; spectrally stable ... See more keywords