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- W4287162907 abstract "We examine the spectral stability and instability of periodic traveling waves for regularized long-wave models. Examples include the regularized Boussinesq, Benney--Luke, and Benjamin--Bona--Mahony equations. Of particular interest is a striking new instability phenomenon -- spectrum off the imaginary axis extending into infinity. The spectrum of the linearized operator of the generalized Korteweg--de Vries equation, for instance, lies along the imaginary axis outside a bounded set. The spectrum for a regularized long-wave model, by contrast, can vary markedly with the parameters of the periodic traveling waves. We carry out asymptotic spectral analysis to short wavelength perturbations, distinguishing whether the spectrum tends to infinity along the imaginary axis or some curve whose real part is nonzero. We conduct numerical experiments to corroborate our analytical findings." @default.
- W4287162907 created "2022-07-25" @default.
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- W4287162907 date "2021-05-31" @default.
- W4287162907 modified "2023-09-27" @default.
- W4287162907 title "Superharmonic instability for regularized long-wave models" @default.
- W4287162907 doi "https://doi.org/10.48550/arxiv.2105.15099" @default.
- W4287162907 hasPublicationYear "2021" @default.
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