7 problems

Let $\tau_{l,m,n}^{(N)}$ be the positive-definite Hankel-determinant $\tau$-function constructed from $M$ parameters $0<p_1<\cdots<p_M$, with $1\leq N\leq M-1$. An $(N_+,N_-)$-soli…

Consider the two-soliton solution of the four-dimensional Wess-Zumino-Witten model and its associated nonlinear sigma-model action density. A V-shape soliton is the soliton profile…

Let $\mathcal{D}^{\mathrm{par}}$ be a compactification of Minkowski space, let $W^{\mathrm{sup}}$ be the supercritical ground-state soliton, and let $z\in\mathbb{R}^3$. Define … A…

Fix distinct soliton speeds, and let $f_{\mathrm{start}}$ denote the starting error whose leading behavior at one soliton is $t^{-1}$. Let $W_a$ be ground-state solitons, let…

Let $\phi$ solve the three-dimensional energy-critical wave equation and satisfy the no-outgoing-radiation condition, and consider multi-solitons whose ground-state components are…

Existence conjecture. Non-symmetric logarithmic $2$-solitary waves exist for the scalar equation whenever $p\neq 3$.

The complex short pulse equation admits an $N$-breather solution given by the determinant formula above, with $M$ and $G$ as defined there. N-breather law conjecture. The $N$-breat…