Bhagavad-Gita: Chapter 10, Verse 31

Rudra Vaisnava Sampradaya:

Visnuswami

Sridhara Swami's Commentary

Of purifiers Lord Krishna's vibhuti or divine, transcendental opulence is the wind. Of wielders of weapons His vibhuti is Parasurama who slew in battle all the ksatriyas or warriors class 21 times with His mighty axe. Among fish His vibhuti is a particular fish that can swallow a whole whale and lives in the deepest part of the ocean known as Makara and amongst all rivers, Lord Krishna's vibhuti is jahnavi a name of the holy Ganga.

Brahma Vaisnava Sampradaya:

Madhvacarya

Madhvacarya's Commentary

Being of the form of ananda or bliss, being completely spiritual of Himself, being the delighter of the people Lord Krishna's vibhuti or divine, transcendental opulence is known as Rama. In the Shandilya section it states: Of blissful form, unlimited, from whom the world revels is known as Rama. Ra and ama are the root and together as Rama mean exceedingly pleasing to all.

Sri Vaisnava Sampradaya:

Ramanuja

Ramanuja's Commentary

Lord Krishna reveals that of things that purify and things that are the swiftest His vibhuti or divine, transcendental opulence is the wind. The words sastra-bhrtam means weapon wielding heroes of which His vibhuti is Rama but unlike other vibhuti which are indirect. Rama is an avatar or direct incarnation of the Supreme Lord Krishna who manifests Himself as Rama the paragon of weapon wielding heroes. Indirect vibhutis such as the Maruts or the Vasus are still jivas or embodied souls even though imbued with a filament of the Supreme Lords potency. In relationship to the Supreme Lord they are exactly like potencies serving Him as the weapons wielded by Rama are likewise serving Him.

Kumara Vaisnava Sampradaya:

Nimbaditya

Kesava Kasmiri's Commentary

Among purifiers Lord Krishna's vibhuti or divine, transcendental opulence is the swift moving wind. Among weapon wielding warriors His vibhuti is the valiant hero Rama who is a lila avatar or divine pastime incarnation of the Supreme Lord Krishna being His catur-vyuya expansion Vasudeva. One should never think that Rama born of King Dasaratha in the solar line of the exalted Raghu dynasty is non-different from the Supreme Lord Krishna except in rasa or mood. The word Rama may also be interpreted to be Parasurama the son of Jamadagni and Renuka, who was a sakyavesa avatar or empowered incarnation of Lord Krishna who slew all the ksatriyas 21 times with His mighty axe. Among rivers His vibhuti is jahnavi the daughter of the sage Jahnu known as the holy river Ganges.