Riemann-Hilbert Problems with canonical normalization and families of commuting operators

doi:https://doi.org/10.48550/arxiv.1204.2928

Open AccessPreprint10.48550/arxiv.1204.2928

Riemann-Hilbert Problems with canonical normalization and families of commuting operators

Vladimir S. Gerdjikov-2012-04-13-arXiv (Cornell University)

TL;DRAbstract

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.

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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

Normalization (sociology)Integrable systemMathematicsConstruct (python library)Ordinary differential equationPure mathematicsRiemann hypothesisNonlinear system

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