New frontiers in dispersive integrable equations

This AIM workshop, sponsored by AIM and the NSF, studies integrable models for dispersive Hamiltonian partial differential equations, a landscape reaching from water waves to nonlinear optics, with questions from well-posedness to long-time dynamics and asymptotic limits in deterministic and random settings. Integrable equations such as the Korteweg-de Vries and nonlinear Schrödinger equations have served as guideposts for nearly 60 years because integrability yields precise results. The main topics are long-time asymptotics of integrable and near-integrable equations, including soliton resolution for equations with nonlocality, higher dimensionality or multiple components and solutions outside the "solitons plus radiation" dichotomy; explicit formulas expressing solutions directly in terms of initial data, their scope, periodic analogues and links to Riemann-Hilbert methods; and soliton gases as models for turbulence, including randomness on initial data and kinetic theory based on collision phase shifts. As an AIM-style workshop it combines background lectures on posted open problems with discussion and parallel working sessions.