Reduced Maxwell–Bloch equations with anisotropic dipole momentum

Abstract

We develop the inverse scattering transform for the recently found integrable system of reduced Maxwell–Bloch equations with two components of polarization and with an anisotropic dipole momentum. The model describes few-cycle pulses of optical or other field propagations. We find that the existence of a nontrivial group of symmetry of the corresponding Lax pair leads to a particular form of the inverse scattering transform equations. We show that solutions can be expressed in terms of the solution of a matrix Riemann–Hilbert problem formulated for the complex plane with a nontrivial group of automorphisms.