Work

Spectral Stability of Travelling Waves in a δ-Regularized Dissipative Sine-Gordon Equation

Year: 2026

Type: article

Abstract: We analyze the spectral stability of travelling waves in a δ-regularized dissipative sine-Gordon equation modelling refined long Josephson junction dynamics. Linearization about a wave yields a singularly perturbed fourth-order spectral problem with intrinsic slow–fast spatial structure. Using an Evans-function formulation on a domain of consistent spatial splitting, we establish a local factorization separating slow and fast modes and prove that the δ-induced fast subsystem remains uniformly hyperbolic and does not generate an additional point spectrum near λ=0. Hence, the local point spectrum coincides with that of the classical dissipative sine-Gordon equation. Numerical computations of the essential spectrum and Evans winding numbers confirm the analysis and show that the higher-order terms enhance high-frequency damping without altering low-frequency spectral stability.

Source: Symmetry

DOI: 10.3390/sym18030512

Author: Vassilios M. Rothos

Institution: Aristotle University of Thessaloniki

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: Aristotle University of Thessaloniki, Research Committee, Aristotle University of Thessaloniki