ε 對於q-KdV階層系統一孤立子和二孤立子解的修正

Abstract

在這篇論文裡透過使用q-deformed的pseudodifferential 算子我們研究Darboux -Backlund轉換(DBTs)應用在 q-deformed Korteweg–de Vries 階層系統。 算子T 是由滿足特定線性系統的波函數所構成，有了這個T可以帶動DBTs的轉換。為了從舊的解去得到新的解 ，我們必須選擇一定特定的算子。反覆疊帶DBTs的轉換，我們獲得one soliton和two solitons的解。另外利用假設q趨近於一(這時q-KdV會回到原本的KdV)和ε等於q減一的假設我們也算出ε對於q-KdV階層系統一孤立子和二孤立子解的修正 。

In this thesis we study Darboux -Backlund transformations (DBTs) for the q-deformed Korteweg -de Vries hierarchy by using the q-deformed pseudodifferential operators. The elementary DBTs are triggered by the gauge operators T constructed from the wave functions of the associated linear systems. In order to obtain the new solution from the old one , we have to choose certain gauge operator. Iterating these elementary DBTs, we obtain one and two solitons solutions. In addition we also figure out the ? correction of one and two solitons for the KdV hierarchy by letting ε equal to q − 1 and q approach 1(which will recovers q-KdV to the ordinary KdV).