We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
37/2001
Classification of solutions of a Toda system in R^2
Jürgen Jost and Guofang Wang
Abstract
In this paper, we consider solutions of the following (open) Toda system (Toda lattice) for SU(N+1) $$-\frac{1}{2} \Delta u_i = \sum\limits^{N}_{j=1} a_{ij} e^{u_j} \ in \ \mathbb{R}^2$$ for $i=1,2,...,.=N$, where $K=(a_{ij})_{N\times N}$ is the Cartan matrix for SU(N+1). We show that any solution $u=(u_1 , u_2 , ... ,u_N)$ with $$\int_{\mathbb{R}^2} e^{u_i} < \infty, \ \ \ i=1,2,...,N,$$ can be obtained from a rational curve in $\mathbb{C} P^N$.
