Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.08128 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910617645875200 |
|---|---|
| author | Bhavna Johnson, Mathew A. Pandey, Ashish Kumar |
| author_facet | Bhavna Johnson, Mathew A. Pandey, Ashish Kumar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08128 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Modulational Instability in the Ostrovsky Equation and Related Models Bhavna Johnson, Mathew A. Pandey, Ashish Kumar Analysis of PDEs 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. |
| title | Modulational Instability in the Ostrovsky Equation and Related Models |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.08128 |