Instability dynamics in the vector pure-quartic dissipative systems

In this work, we analytically investigate, for the first time, instability dynamics induced by pure-quartic dispersion in vector dissipative systems governed by vector complex Ginzburg–Landau equations (CGLEs) that incorporate pure-quartic dispersion, four-wave mixing, and gain–loss effects. The vector CGLEs describe pulse propagation and evolution in all-optical mode-locked fiber laser configurations with pure-quartic dispersion. A modified linear stability analysis is employed to examine modulation instability (MI) arising from small perturbations to continuous-wave steady states. Using the analytical results, we systematically explore how key physical parameters, including wave-number mismatch, pure-quartic dispersion, nonlinearity, gain bandwidth, and gain coefficient, affect the MI process and overall instability characteristics. The analysis is performed rigorously for both gain-free (a regime of the proposed model not previously reported) and dissipative systems. Notably, we uncover distinct instability signatures, including asymmetric MI sidebands, monotonically increasing sideband gain, rectangular spike-like spectra, and partially blown-out MI structures in dissipative systems.