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Abstract

We develop an adiabatic theory for strongly chirped dissipative solitons governed by the cubic-quintic complex Ginzburg-Landau equation and analyze their existence regions in both normal and anomalous dispersion regimes. Closed-form expressions for the frequency cut-off and peak power yield two physical branches whose admissibility is set by a compact dimensionless parameterization. The analysis reveals that dissipative-soliton resonance (chirp-driven temporal stretching with bounded peak power) naturally emerges on the scalable branch, providing a direct pathway to high-energy femtosecond oscillators without external amplification. We interpret these results within a thermodynamic framework that connects energy "condensation" in the soliton to a BEC-like metaphor, providing quantitative indicators for energy scalability limits and breakup onsets, and aligning with a recently formulated thermodynamic methodology for dissipative solitons. Beyond immediate laser design guidance, our approach suggests a generalized thermodynamic theory of strongly chirped dissipative solitons, including measurable entropy and temperature proxies, as well as a phase diagram that distinguishes between single- and multi-soliton states. This unifies practical laser engineering criteria with many-body concepts, pointing to optics-based, metaphorical simulations of condensate phenomena.