Work

Modulational instability of small amplitude periodic traveling waves in the Novikov equation

Year: 2025

Type: article

Abstract: We study the spectral stability of smooth, small-amplitude periodic traveling wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearities. Specifically, we investigate the L2(R)-spectrum of the associated linearized operator, which in this case is an integro-differential operator with periodic coefficients, in a neighborhood of the origin in the spectral plane. Our analysis shows that such small-amplitude periodic solutions are spectrally unstable to long-wavelength perturbations if the wave number is greater than a critical value, bearing out the famous Benmajin-Feir instability for the Novikov equation. On the other hand, such waves with wave number less than the critical value are shown to be spectrally stable. Our methods are based on applying spectral perturbation theory to the associated linearization.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0240100

Authors: Brett Ehrman, Mathew A. Johnson, Stéphane Lafortune

Institutions: University of Kansas, College of Charleston

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation

Awards: G1186376312, Modulations of Periodic Waves in Applied Mathematics