Strongly chirped dissipative solitons in normal and anomalous dispersion regimes

We study strongly chirped dissipative solitons (DSs) of the cubic--quintic complex Ginzburg--Landau equation (CGLE) in both normal- and anomalous-group-delay dispersion regimes (NGD and AGD). Using a stationary-phase (adiabatic) approximation, we obtain analytic NGD and AGD spectra, allowing us to represent the DS parametric space as a master diagram that connects ratios of spectral filter parameters, group-delay dispersion (GDD), and self-phase (SPM) and self-amplitude (SAM) modulations to a scaled DS energy. A central result is that dissipative-soliton resonance (DSR) emerges in the NGD and follows directly from the admissibility constraints, whereas, in the AGD, it appears only when the DSR locus intersects the adiabatic existence window. The last requires sufficiently strong quintic (saturable) SPM.In the NGD, the spectra are inherently truncated. In the AGD, the spectral envelopes are approximately self-similar in an energy-scaling regime, have two-horns, smooth wings, and frequency truncation is provided by a spectral dissipation. In this regime, the energy dependence is captured predominantly by a scalar prefactor, while the unit-peak spectral core remains nearly invariant.We demonstrate that, in AGD, there is a separation between the absolute first-order autocorrelation magnitude and the normalized coherence shape, revealing two distinct correlation times: a short scale set by the effective spectral dissipation bandwidth and a long scale controlled by the intrinsic spectral core, as in NGD.Finally, we outline a thermodynamic interpretation of the correlation-scale separation and its connection to an entropy-driven transition between single- and multi-soliton states, thereby constraining the DS energy scalability. We also discuss how the same two-scale coherence phenomenology can be relevant to weakly dissipative Bose-Einstein condensate (BEC) settings (atomic and driven optical condensates) in the presence of bandwidth-limited spectral and/or linear and nonlinear losses.