5 problems

Let $N \ge 1$ be an integer and let $\varepsilon > 0$. Suppose $u_0 \in L^2(\mathbb{T})$ is frequency-localized as … Let $u(x,t)$ be the corresponding solution to the periodic line…

Let $\eta=\{\eta_k\}_{k\geq1}$ and $\eta^{(1)}=\{\eta_k^{(1)}\}_{k\geq1}$ be the frequency collections associated with the comb domains describing the KdV flows. Comb-domain generi…

Let $\mathsf{E}$ be the spectral set, let $\mathcal{R}(\mathsf{E})$ denote the reflectionless potentials with spectrum $\mathsf{E}$, and let … be the divisor map. Let…

Let $m\in\mathbb{N}$ and $\tilde{c}>0$. For sufficiently small $\varepsilon>0$, consider the FPU system and the speed $c=1-\varepsilon^2\tilde{c}$. A generalized moving pulse solut…

Let $u(x)$) and $y(x)$ be functions satisfying equation … possesses four step-like solutions for any $H_0>-4$ and $H_1>0$. Two of them have the asymptotic behaviour … and another t…