4 problems

Let a weakly nonlinear dispersive flow evolve from generic initial data. Soliton resolution conjecture. As $t\to+\infty$, the solution should split asymptotically into a finite col…

The Landau–Lifshitz model is an integrable $(1+1)$-dimensional soliton system, and its classical–quantum correspondence concerns the relation between its classical dynamics and the…

Let the original nonlinear system have a set of symmetries, and let its associated linear system have another set of symmetries. In the finite-dimensional case, compare these sets…

Let $q$ be an initial datum such that the associated operator $\mathbb{L}_{q}$ has some negative essential spectrum. The behavior under consideration is the asymptotic splitting of…