Work

Floquet theory and stability analysis for Hamiltonian PDEs

Year: 2024

Type: article

Abstract: We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs, including the generalized KdV and BBM equations (third order), the nonlinear Schrödinger and Boussinesq equations (fourth order), and the Kawahara equation (fifth order). Our analysis reveals that the characteristic polynomial of the monodromy matrix inherits symmetry from the underlying PDE, enabling us to determine the essential spectrum along the imaginary axis and bifurcations of the spectrum away from the axis, employing the Floquet discriminant. We present numerical evidence to support our analytical findings.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ad8698

Authors: Jared C Bronski, Vera Mikyoung Hur, Robert Marangell

Institutions: University of Illinois Urbana-Champaign, The University of Sydney

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,165

Funders: Simons Foundation, Directorate for Mathematical and Physical Sciences, Australian Research Council