---
abstract: |
    We first study coupled Hirota-Iwao modified KdV (HI-mKdV) systems and give all possible local and nonlocal reductions of these systems. We then present Hirota bilinear forms of these systems and give one-soliton solutions of them with the help of pfaffians. By using the soliton solutions of the coupled HI-mKdV systems for $N=2,3,$ and $N=4$ we find one-soliton solutions of the local and nonlocal reduced equations.\
    **Keywords:** Ablowitz-Musslimani reduction, Nonlocal coupled Hirota-Iwao modified\
    Korteweg-de Vries equations, Hirota bilinear form, Pfaffians, Soliton solutions.
author:
- |
    Asl[i]{} Pekcan [^1]\
    [Department of Mathematics, Faculty of Science]{}\
    [Hacettepe University, 06800 Ankara - Turkey]{}
date:
- 
- 
title: 'Nonlocal Coupled HI-MKdV Systems'
---

ł@paragraph[dottedtocline[4]{}[5.3em]{}[2.1em]{}]{}

Introduction
============

In last decade, it has been shown by many researchers that by using different local and nonlocal symmetry reductions one can obtain local and the time reflection symmetric (T-symmetric), the space reflection symmetric (S-symmetric), and the space-time reflection symmetric (ST-symmetric) nonlocal equations from the general AKNS formalism [@AKNS] and other integrable hierarchies. The main aim in these works is to find new integrable equations and to obtain new interesting wave solutions. Particular examples are nonlocal nonlinear Schrödinger (NLS) equation [@AbMu1]-[@jianke], nonlocal real or complex modified Korteweg-de 