Matrix Riemann-Hilbert problems and Maxwell-Bloch equations without spectral broadening (Q2878015)

The authors develop a method for the Riemann-Hilbert problem for the Maxwell-Bloch equations. The method is related to the inverse scattering transform and Marchenko's integral equations and has not been applied before to mixed problems. The Riemann-Hilbert problem consists of the determination of the \(2\times 2\) matrix functions \(M^{\pm}\) meromorphic in \(\mathbb C^{\pm}\), respectively, with the conjugation condition \(M^{-}=M^{+} J\) on the real axis, where \(J\) is a given piecewise continuous matrix. The type of solutions is defined by the matrix \(J\).