New types of two component NLS-type equations

TL;DR

This paper introduces new two-component NLS-type equations derived from MNLS related to D.III-type symmetric spaces, expanding the class of integrable models with novel interaction Hamiltonians involving mixed terms.

Contribution

The authors derive new 2-component NLS equations using Mikhailov reduction groups, which include interaction terms beyond the standard form, not contradicting the Zakharov-Schulman theorem.

Findings

Derived new 2-component NLS equations with mixed interaction terms

Demonstrated these equations are not counterexamples to the Zakharov-Schulman theorem

Expanded the class of integrable NLS-type models

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 $q_1q_2^* +q_1^* q_2$.