Riemann-Hilbert Problems with canonical normalization and families of commuting operators
arXiv:1204.2928
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.
14 pages, Submitted to Pliska Stud. Math. Bulgar