Modulational instability and variational structure

2013/03/11 by Jared C. Bronski, Bronski, Jared C., Vera Mikyoung Hur +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.48550/arxiv.1303.2605

openalex publication_date 2013/03/11 · arxiv created 2013/06/27 · arxiv updated 2013/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the modulational instability of periodic traveling waves for a class of Hamiltonian systems in one spatial dimension. We examine how the Jordan block structure of the associated linearized operator bifurcates for small values of the Floquet exponent to derive a criterion governing instability to long wavelengths perturbations in terms of the kinetic and potential energies, the momentum, the mass of the underlying wave, and their derivatives. The dispersion operator of the equation is allowed to be nonlocal, for which Evans function techniques may not be applicable. We illustrate the results by discussing analytically and numerically equations of Korteweg-de Vries type.

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