Novel systems of resonant wave interactions

Abstract

A matrix Riemann–Hilbert problem (RHP) is constructed using the dressing method starting from two uncoupled, one-directional linear wave equations; the RHP thus obtained is then used to derive a novel integrable matrix non-local system of equations describing resonant wave interactions, together with its Lax pair. This system is shown to be a matrix generalization of the equations for resonant three-wave interactions and stimulated Raman scattering. Several compatible reductions admitted by this system are also discussed.