Quasi-periodic travelling waves for a class of damped beams on rectangular tori

Multidimensional Stability of Waves Travelling Through Rectangular Lattices in Rational Directions

We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small perturbations. We employ recently developed techniques involving point-wise Green's functions estimates for functional differential equations of mixed type (MFDEs), allowing our results to be applied even in situations where comparison principles are not available.

Analytic solutions of nonlinear elliptic equations on rectangular tori

In this paper, we consider the nonlinear elliptic equations on rectangular tori. Using methods in the study of KAM theory and Anderson localization, we prove that these equations admit many analytic solutions.

非矩形平坦环面上三次非线性薛定谔方程的长时间稳定性

Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori

本文针对满足丢番图非退化条件的平坦环面上的三次非线性薛定谔方程，证明了高正则Sobolev空间中大多数小解的几乎全局存在性与稳定性，并发展了可调制频率的正规形方法。

环面上$\mathbb{Z}^m$作用的矩形收缩目标：良好与不良逼近系统

Rectangular shrinking targets for $\mathbb{Z}^m$ actions on tori: well and badly approximable systems

本文研究了无理旋转的收缩目标性质，采用新方法证明了其加权有效类比，推广了Kim和Shapira的结果，并在更广泛的$S$-arithmetic设定下成立。

Dynamics of curved travelling fronts for the discrete Allen-Cahn equation on a two-dimensional lattice

In this paper we consider the discrete Allen-Cahn equation posed on a two-dimensional rectangular lattice. We analyze the large-time behaviour of solutions that start as bounded perturbations to the well-known planar front solution that travels in the horizontal direction. In particular, we construct an asymptotic phase function $γ_j(t)$ and show that for each vertical coordinate $j$ the corresponding horizontal slice of the solution converges to the planar front shifted by $γ_j(t)$. We exploit the comparison principle to show that the evolution of these phase variables can be approximated by …