Weak soliton resolution for nonlinear Schrödinger equations

The soliton resolution conjecture states that solutions to nonlinear Schrödinger equations decompose into a number of nonlinear bound states (called solitons) and decaying radiation term. Although numerical and physical evidence strongly suggests that the conjecture holds, the set of equations where the conjecture has actually been proven mathematically is currently rather narrow.

In this talk, I will discuss the weak soliton resolution conjecture, which was proposed by Terence Tao in 2008 as a more tractable simplification of the problem.  After giving background on the broader area of scattering theory, which arose to describe processes in molecular, atomic, and high-energy physics, I will explain what the soliton resolution says, and how the weak soliton resolution problem is simpler.  Finally, I will show how to obtain weak soliton resolution for defocusing equations with focusing linear terms.