English

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