2015/08/25 by Zhaohu Nie, Nie, Zhaohu
Mathematics · Physics and Astronomy · #17B80 #35J47 #35J91 #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #math.AP #msc:17B80 #msc:35J47 #msc:35J91 #nlin.SI
paper · pdf · doi:10.48550/arxiv.1508.06188
23 pages
arxiv created 2015/08/25 · arxiv updated 2015/08/26
In this paper, the classification in [Lin,Wei,Ye] of solutions to Toda systems of type A with singular sources is generalized to Toda systems of types C and B. Like in the A case, the solution space is shown to be parametrized by the abelian subgroup and a subgroup of the unipotent subgroup in the Iwasawa decomposition of the corresponding complex simple Lie group. The method is by studying the Toda systems of types C and B as reductions of Toda systems of type A with symmetries. The theories of Toda systems as integrable systems as developed in [Leznov, Saveliev, Nie], in particular the W-symmetries and the iterated integral solutions, play essential roles in this work, together with certain characterizing properties of minors of symplectic and orthogonal matrices.