---
abstract: 'In this paper, we explicitly construct a series of projectors on integral noncommutative orbifold $T^2/Z_4$ by extended $GHS$ constrution. They include integration of two arbitary functions with $Z_4$ symmetry. Our expression possess manifest $Z_{4}$ symmetry. It is proved that the expression include all projectors with minimal trace and in their standard expansions, the eigen value functions of coefficient operators are continuous with respect to the arguments $k$ and $q$. Based on the integral expression, we alternately show the derivative expression in terms of the similar kernal to the integral one. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a series of corresponding solitons.'
author:
- |
    Hui Deng $$\thanks{Email:hdeng@phy.nwu.edu.cn},
    \hspace{5mm}
             Bo-Yu Hou$$ [^1], Kang-Jie Shi$$\thanks{Email:kjshi@phy.nwu.edu.cn},
                             \hspace{5mm}
            Zhan-Ying Yang$$ [^2], Rui-Hong Yue$$ [^3]\
    Institute of Modern Physics, Northwest University,\
    Xi’an, 710069, P. R. China
title: '**Soliton Solutions on Noncommutative Orbifold $ T^2/Z_4 $**'
---

      Soliton, Projection operators, Noncommutative orbifold.

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

String theory is a very promising candidate for an unified description of the fundamental interactions, including quantum gravity. It may provide a conceptual framework to resolve the clash between two of the greatest achievements of 20th century physics: general 