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

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

2004-05-19

arxiv.org/abs/math/0405365v1

Mathematics

Differential Geometry

17 pages

Scientific paper

10.1063/1.1929688

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 $t\to -\infty$.

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