Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators

Abstract

We start with a Riemann-Hilbert Problems (RHP) with canon- ical normalization whose sewing functions depends on several additional vari- ables. 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.