Lord Krishna as He appears once every twenty-four hours of Brahma’s time (or after a lapse of 8,640,000,000 solar years) in each and every universe and all His transcendental pastimes are displayed in each and every universe in a routine spool. But in that routine spool the functions of Lord Krishna, Lord Vasudeva, etc., are complex problems for the layman. There is no difference between the Lord’s Self and the Lord’s transcendental body. The expansions execute differential activities. When the Lord, however, appears in His person as Lord Sri Krishna, His other plenary portions also join in Him by His inconceivable potency called yogamaya, and thus the Lord Krishna of Vrndavana is different from the Lord Krishna of Mathura or the Lord Krishna of Dvaraka. The Virat-rupa of Lord Krishna is also different from Him, by His inconceivable potency. The viratrupa exhibited on the Battlefield of Kuruksetra is the material conception of His form. Therefore it should be understood that when Lord Krishna was apparently killed by the bow and arrow of the hunter, the Lord left His so-called material body in the material world. The Lord is kaivalya, and for Him, there is no difference between matter and spirit because everything is created from Him. Therefore His quitting one sort of body or accepting another body does not mean that He is like the ordinary living being. All such activities are simultaneously one and different by His inconceivable potency. When Maharaja Yudhisthira was lamenting the possibility of His disappearance, it was just in pursuance of a custom of lamenting the disappearance of a great friend, but factually the Lord never quits His transcendental body, as is misconceived by less intelligent persons. Such less intelligent persons have been condemned by the Lord Himself in Bhagavad-gita, and they are known as the mudhas. That the Lord left His body means that He left again His plenary portions in the respective dhamas (transcendental abodes), as He left His Virat-rupa in the material world.
Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, First Canto, Chapter 14 – Text 8