New types of two component NLS-type equations

We study MNLS related to the D.III-type symmetric spaces. Applying to them Mikhailov reduction groups of the type ${\mathbb{Z}}_r\times {\mathbb{Z}}_2$ we derive new types of 2-component NLS equations. These are {\bf not} counterexamples to the Zakharov-Schulman theorem because the corresponding interaction Hamiltonians depend not only on $\mathrm{\mid }{q}_k{\mathrm{\mid }}^2$, but also on $q_1q_2^* +q_1^* q_2$.