7 problems

Soliton resolution conjecture. Any smooth, finite-energy solution $W(t,r)$ tends as $t\to\infty$, modulo sign, either to the half-kink or to a rescaled half-kink together with an a…

Soliton resolution conjecture. Asymptotically, the $(n,t)$-space splits into regions separated by straight lines through the origin. Some regions are periodic, with period equal to…

Let the 3D Zakharov–Kuznetsov equation be given by, and let the soliton solutions be those defined by --. A perturbation is understood to be of soliton-like initial data, and suffi…

Consider a bounded solution $u$ of the focusing energy-critical nonlinear wave equation (NLW). A soliton resolution conjecture predicts that, as time approaches the maximal time of…

Non-equivariant soliton resolution conjecture. The unique wave-map evolution associated with $(u_0,u_1)$ is globally regular and scatters to $(\mathcal{P}_\lambda,0)$ as…

Soliton resolution conjecture. The Cauchy problem is globally well-posed, and its solution scatters to $P_\lambda$ as $t\to\pm\infty$. The harmonic maps $P_\lambda$ minimize the en…

Consider the critical wave equation in three spatial dimensions, and let $u$ be a radial energy class solution with energy close to the ground-state energy $E(W,0)$, where $W$ deno…