Exact Solutions and Stability Analysis of Pulse-Front Pairs in Coupled Complex Ginzburg–Landau Equations

Abstract

This work introduces new exact solutions demonstrating how localized pulses and fronts can coexist in coupled complexGinzburg–Landau systems. Using a novel analytical method, we establish conditions for the stability and phase-lockingof these structures, revealing relationships between amplitude, wave-number, and dispersion effects. In practical opticalsetups like dual-core fibers, these solutions can produce stable wave patterns that transfer energy efficiently. Ourapproach addresses existing difficulties in analyzing complex dissipative systems and enhances understanding of theirwave interactions