The conference, in advance of a thematic program planned for IHP in 2026, addresses the key role played by completely integrable systems as models for wave phenomena in myriad physical settings such as surface water waves and internal waves, quantum excitations in Bose-Einstein condensates, plasma oscillations, optical fiber telecommunication systems, and solid-state physics. The principal objectives of the CIRM conference are to focus specifically on soliton gases, explicit formulas, and asymptotic behavior in integrable models, and to highlight corresponding novel results and new progress on several previously impenetrable fronts. By sharing these new ideas with colleagues, junior researchers, and students, conference participants will forge new collaborations and mentorship opportunities that will lay the groundwork for a largerscale IHP program the following year. The conference will also allow participants to identify the most promising research avenues and to influence the agenda for the IHP program. The main impacts of the proposed conference will be (1) the propagation of new scientific ideas related to soliton gas theory, properties of explicit solutions of integrable wave models, and the asymptotic analysis of such models in large-time or weakly-dispersive limits; (2) the inclusion of a scientifically broad and culturally diverse cohort of participants which is already part of the historical context of the area of the conference; (3) the promotion and planning of the 2026 IHP program.