Maulana Dawood Raz
Hadith Commentary:
In Sahih Muslim, it is narrated directly from the Prophet sallallahu alayhi wa sallam that Kawthar is a river which Allah has granted to me.
A general interpretation has also been made with the phrase "abundant good" (khayr kathir).
Hafiz (rahimahullah) says: "And the commentators have transmitted in the explanation of Kawthar statements other than these two, exceeding ten in number," i.e., the commentators have reported more than ten interpretations regarding Kawthar: Prophethood, the Qur'an, Islam, monotheism (tawhid), abundance of followers, self-sacrifice (ithar), elevation of mention, illumination of the heart, intercession (shafa'ah), miracles, acceptance of supplication (ijabat du'a), understanding of religion (fiqh fi al-din), the five prayers (salawat al-khams), etc.—all of these have been mentioned in the interpretation of Kawthar.
In reality, what is meant by it is the Hawd Kawthar (the Pond of Kawthar), and secondarily, all these virtues that have been mentioned have indeed been granted by Allah to His beloved, which can be expressed under the phrase "abundant good" (khayr kathir) as signified by the word Kawthar.
For details, refer to Fath al-Bari.
Source: Sahih Bukhari: Commentary by Maulana Dawood Raz, Page: 4966
Shaykh Abdul Sattar al-Hammad
Hadith Commentary:
Kawthar, in its linguistic sense, is derived from "abundance."
By it is meant abundant good, as will be explained further by Ibn Abbas radi Allahu anhu.
It has such generality that other meanings are also included within it, such as the river of Kawthar in Paradise, which is also a part of this abundant good. Likewise, in the hadith, the Pond of Kawthar is also mentioned as an instance of this.
The believers will drink its water from the blessed hand of the Messenger of Allah sallallahu alayhi wa sallam before entering Paradise.
(Sahih al-Bukhari, al-Riqaq, Hadith: 6579)
The water in this Pond will be coming from that river in Paradise.
Similarly, the conquests in this world, the elevation and exaltation of your rank, and the perpetuity of your mention are also included in this abundant good.
And Allah knows best.
Source: Hidayat al-Qari: Commentary on Sahih Bukhari, Urdu, Page: 4966