Riemann-Hilbert Problems with canonical normalization and families of commuting operators
Exactly Solvable and Integrable Systems
2012-04-16 v1
Abstract
We start with a Riemann-Hilbert Problems (RHP) with canonical normalization whose sewing functions depends on several additional variables. Using Zakharov-Shabat theorem we are able to construct a family of ordinary differential operators for which the solution of the RHP is a common fundamental analytic solution. This family of operators obviously commute. Thus we are able to construct new classes of integrable nonlinear evolution equations.
Keywords
Cite
@article{arxiv.1204.2928,
title = {Riemann-Hilbert Problems with canonical normalization and families of commuting operators},
author = {Vladimir S. Gerdjikov},
journal= {arXiv preprint arXiv:1204.2928},
year = {2012}
}
Comments
14 pages, Submitted to Pliska Stud. Math. Bulgar