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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
45/2005

Analytic Aspects of the Toda System: II. Bubbling behavior and existence of solutions

Jürgen Jost, Chang-Shou Lin and Guofang Wang

Abstract

In this paper, we continue to consider the 2-dimensional (open) Toda system (Toda lattice) for $SU(N+1)$ \begin{equation}- \Delta u_i = \sum_{j=1}^N a_{ij} e^{u_j}, \end{equation} for $i=1,2,\cdots, N$, where $K=(a_{ij})_{N\times N}$ is the Cartan matrix for $SU(N+1)$ given by \[ \left(\begin{array}{rrrrrr} 2 & -1 & 0 & \cdots & \cdots & 0\cr -1& 2 &-1& 0 & \cdots & 0\cr 0&-1&2&-1& \cdots & 0\cr \cdots&\cdots&\cdots&\cdots&\cdots&\cdots\cr 0 &\cdots&\cdots& -1&2&-1\cr 0&\cdots&\cdots & 0 &-1&2\cr\end{array}\right).\nonumber\] we give a much more precise bubbling behavior of solutions and consider its existence in some critical cases

Received:
May 9, 2005
Published:
May 9, 2005
MSC Codes:
35J60
Keywords:
toda system, bubbling behavior, chern-simons theory

Related publications

inJournal
2006 Repository Open Access
Jürgen Jost, Changshou Lin and Guofang Wang

Analytic aspects of the Toda system. Pt. 2 : Bubbling behavior and existence of solutions

In: Communications on pure and applied mathematics, 59 (2006) 4, pp. 526-558