标题： 周期解和修正的2+1手征模型的同宿解 显示英文标题

标题： Periodic and homoclinic solutions of the modified 2+1 Chiral model

摘要： 我们使用代数Bäcklund变换(BTs)从$T^2\times R$构造到SU(n)的修正2+1维手征模型的显式解，其中$T^2$是一个2环面。代数BTs由$z\in C$(极点)和从$T^2$到Gr$(k,C^n)$的全纯映射$\pi$参数化。 我们应用具有精心选择极点和$\pi$的 Bäcklund 变换，以构造 2+1 色散模型的无限多解，这些解满足：(i) 在空间变量上双重周期且在时间上周期，即三重周期，(ii) 同宿于这样的解$u$，其具有与$t\to \pm\infty$相同的定态极限$u_0$，并且当$t\to\infty$时与$u_0$的稳定线性模态相切，当$t\to -\infty$时与$u_0$的不稳定模态相切。 显示英文摘要

摘要： We use algebraic Backlund transformations (BTs) to construct explicit solutions of the modified 2+1 chiral model from $T^2\times R$ to SU(n), where $T^2$ is a 2-torus. Algebraic BTs are parameterized by $z\in C$ (poles) and holomorphic maps $\pi$ from $T^2$ to Gr$(k,C^n)$. We apply B\"acklund transformations with carefully chosen poles and $\pi$'s to construct infinitely many solutions of the 2+1 chiral model that are (i) doubly periodic in space variables and periodic in time, i.e., triply periodic, (ii) homoclinic in the sense that the solution $u$ has the same stationary limit $u_0$ as $t\to \pm\infty$ and is tangent to a stable linear mode of $u_0$ as $t\to\infty$ and is tangent to an unstable mode of $u_0$ as $t\to -\infty$.