Soliton resolution in dispersive equations


Speaker: Prof. Hao Jia(University of Minnesota)




A remarkable feature for dispersive equations is the ``simplification" of solutions at large times. For linear dispersive equations, this is well understood. But for nonlinear equations where there are complicated solitary waves, the mechanism by which the solution ``de-couple" into the solitary waves plus radiation is still mysterious, except for integrable systems. We will review some history on this fascinating topic, and explain some recent progress in the energy critical wave equations, such as defocusing wave with potential, focusing wave equations, and wave maps.