Exact Solutions and Stability Analysis of Pulse-Front Pairs in Coupled Complex Ginzburg–Landau Equations - YEE, Tat Leung (JOURNAL OF ADVANCES IN MATHEMATICS, 2025)
This work introduces new exact solutions demonstrating how localized pulses and fronts can coexist in coupled complex Ginzburg–Landau systems. Using a novel analytical method, we establish conditions for the stability and phase-locking of these structures, revealing relationships between amplitude, wave-number, and dispersion effects. In practical optical setups like dual-core fibers, these solutions can produce stable wave patterns that transfer energy efficiently. Our approach addresses existing difficulties in analyzing complex dissipative systems and enhances understanding of their wave interactions.