Abstract
There are many problems in pure and applied mathematics that can be solved in terms of a Riemann-Hilbert (R-H problem). The list includes the remarkable class of nonlinear integrable equations, namely nonlinear equations that can be written as the compatibility conditions of linear equations. This class contains a large variety of equations: ODE’s, PDE’s difference equations, etc. Furthermore, the R-H problem formulation provides a powerful technique for obtaining asymptotic results for solutions of ODE’s and PDE’s of this class [1].
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Enolskii, V., Grava, T. (2006). RIEMANN-HILBERT PROBLEM AND ALGEBRAIC CURVES. In: Faddeev, L., Van Moerbeke, P., Lambert, F. (eds) Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete. NATO Science Series, vol 201. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3503-6_7
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