Ram travelled from the Gangetic plains to the southern coast 7,000 years ago, while Krishna migrated from the Gangetic plains to the western coast 5,000 years ago. This is traditional lore, based on astrological information. However, this is not based on what historians consider evidence.
At the Maharaja Sayajirao University Oriental Institute of Baroda, various versions of the oldest Ramayana have been collected from different parts of India. Scholars used this archive to put together a critical edition of the Ramayana, compiling verses they felt to be the oldest and most authentic. In this version, there is no mention of ‘Lakshman Rekha’; Ravana simply picks Sita up in the absence of Ram and Lakshman. Likewise, at the Bhandarkar Oriental Research Institute, Pune, a critical edition from the oldest extant versions of the Mahabharata was put together by scholars. In this version, Krishna does not come to Draupadi’s rescue in the gambling hall; bad omens force the Kauravas to stop. Of course, scholars disagree on which verses constitute the earliest versions and which do not.