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arXiv · 2305.08128

Modulational Instability in the Ostrovsky Equation and Related Models

Bhavna·Mathew A. Johnson·Ashish Kumar Pandey
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Abstract

We study the modulational instability of small-amplitude periodic traveling wave solutions in a dispersion generalized Ostrovsky equation. Specifically, we investigate the invertibility of the associated linearized operator in the vicinity of the origin and derive a modulational instability index that depends on the dispersion and nonlinearity. For the classical Ostrovsky equation, we recover the well-known Lighthill condition for modulational instability of small-amplitude periodic traveling waves, and further provide a rigorous connection of the Lighthill condition to the spectral instability of the underlying wave. Our results and methodologies further apply to a wide-class of Ostrovsky type models that incorporate various dispersive effects. As such, we present new results illuminating the effects of rotation on various full-dispersion models arising in the study of weakly nonlinear surface water waves.

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Bhavna, Mathew A. Johnson, Ashish Kumar Pandey. 2023-05-14. Modulational Instability in the Ostrovsky Equation and Related Models. https://arxiv.org/abs/2305.08128

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