7 problems

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…

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…

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…

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…

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…