Riemann-Hilbert problem, integrability and reductions

The present paper is dedicated to integrable models with Mikhailov reduction groups $G_R\simeq {\mathbb{D}}_h\mathrm{.}$ Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the $G_R$-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with ${\mathbb{D}}_h$ symmetries are presented.