Problem in an authentic hadith

Assalamu alaikum, there is a hadith, sahih bukhari 3618 , that has been in my mind for a while. So here it is : > "Allah's Messenger (ﷺ) said, "When Khosrau perishes, there will be no (more) Khosrau after him, and when Caesar perishes, there will be no more Caesar after him. By Him in Whose Hands Muhammad's life is, you will spend the treasures of both of them in Allah's Cause." So as you can see here the prophet Muhammad S.A.W prophecies that when the current khosrow (i.e persian king) perishes or dies, there will be no khosrow after him, this is true and actually happened as when Yazdegered III died during the islamic conquest of persia, there was no more persian kings after him and his dynasty was extinguished. Now in the rest of the hadith, the prophet says that when Caesar (i.e Roman emperor) dies, there will be no more Roman emperor after him. But, historically there were a multitude of Roman emperors after Heraclius (The Roman emperor during the time of the prophet p.b.u.h) up until 1453 at the fall of constantinople. How to understand this seeming difficulty? I kindly ask for your answers if you have a good explanation. Walaykum assalam.