New types of two component NLS-type equations

Abstract

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 $|q_k{|}^2$, but also on $q_1{q}_2^{\ast }+q_1^{\ast }{q}_2$.

14 pages