此篇論文主要在描述維持向量型非線性自相似子的條件和解析與數值過程。自相似子在描述一種光波，其形狀隨著傳播距離仍維持基本雛形，但是某些波的參數像是振幅、相位、位置...等等會隨著系統參數像是濾波和增益而改變。此論文用到的向量模型公式除了基本非線性薛丁格方程式所具有的繞射(或色散)項與三次非線性項，還具有濾波項(在橫向為二次方函數而縱向為特徵濾波函數)，增益或損耗項這些項存在。
利用的技巧首先將一個分離變數的解形式代入向量型模型公式中，將解代入後展開後，利用實部和虛部，光孤子解和二次方函數的獨立性等相關解析技巧可以建構出相關公式。
比較特別的是雖然非線性薛丁格方程式有亮-亮光孤子對、暗-暗光孤子對、暗-亮光孤子對存在，但是因為導正過程中會出現非線性薛丁格方程式兩偏振態的強度分布必須要成比例這條件，所以對應到自相似子對僅有亮-亮自相似子對和暗-暗自相似子對存在。另外，向量型自相似子對不同於純量型自相似子對，它的存在性必須滿足一個由兩偏振態寬度比值平方與交互相位調變係數所形成的係數空間。
實驗上，先要找到滿足某種目地的兩偏振態的尺度函數，然後就可以依照公式求出隨傳播距離而變的增益函數與濾波函數來控制。
總結來說，具有自相似性特徵的光波在漸變折射率非線性光波導中增益器中交互作用後會維持他們的本體，而這篇論文顯示僅有亮-亮自相似子對和暗-暗自相似子對存在，而它們可以一對一地對應到向量模型的非線性薛丁格方程式。

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