Nonabelian Integrable Systems, Quasideterminants, and Marchenko Lemma
Abstract
We find explicit (multisoliton) solutions for nonabelian integrable systems such as periodic Toda field equations, Langmuir equations, and Schrodinger equations for functions with values in any associative algebra. The solution for nonabelian Toda field equations for root systems of types A, B, C was expressed by the authors in a previous paper (q-alg/9701008) using quasideterminants introduced by the last two authors. To find multisoliton solutions of periodic Toda equations and other nonabelian systems we use a combination of these ideas with important lemmas which are due to Marchenko.
Cite
@article{arxiv.q-alg/9707017,
title = {Nonabelian Integrable Systems, Quasideterminants, and Marchenko Lemma},
author = {Pavel Etingof and Israel Gelfand and Vladimir Retakh},
journal= {arXiv preprint arXiv:q-alg/9707017},
year = {2008}
}
Comments
10 pages, amstex; in the new version, a misprint in the formula before Proposition 2 was corrected, and a few very minor changes were made; a reference was added