TITLE:
Controlling Nonlinear Signal Amplification in Superconductors via Modulational Instability
AUTHORS:
Paldou Yaya Alexis, Essebe Eba David, Kamdem Tamwa Romuald, Kol Guy Richard
KEYWORDS:
Modulational Instability, Superconductors, Nonlinear Waves, Signal Dynamics, Complex Ginzburg-Landau Equation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.9,
September
14,
2026
ABSTRACT: We investigate nonlinear signal propagation in superconducting media using the complete complex Ginzburg-Landau equation. A perturbative modulational instability framework is employed to derive analytical expressions for the dispersion relation and growth rate. The analysis reveals well-defined instability domains where small perturbations are exponentially amplified, giving rise to high-amplitude localized breather structures. Group velocity dispersion and phase self-modulation govern the transition between stable and unstable regimes. The growth rate exhibits maxima corresponding to optimal conditions for energy localization and signal amplification; outside these regions, the system supports stable, low-amplitude periodic waves. This analytical framework opens perspectives for the design of superconducting devices, photonic technologies, and advanced signal processing applications.