Nowhere in Ramayana we find the names of the rivers "Krishna, Tungabhadra, and Cauvery" which are fairly wide and long rivers, without crossing which it is not possible to travel from Vindhya Hills (Central India)to Sri Lanka in Indian Ocean. Though there are legends linking Sri Lanka with Ramayana, it is difficult to rely on them unless there is proof.
Note: There is a reference to river Godavari in 3-15-12. Rama and Lakshmana built their cottage on the banks of river Godavari, at a place called Panchavati.
Iyam Godaavarii ramyaa pushpitaihi tarubhir vrutaaiyam = This is river Godavari, surrounded by plants blooming with flowers.
PART 4, CHAPTER 52, VERSEs31 and 32, SANSKRIT:
Eesha vinhdhyoo girihi shriimaan naanaa druma lataa aayutaha
eesha prasavan`aha shailaha saagaro ayam mahaa udadhihi
svasti vo astu gamishyaami bhavanam vaanararshabhaaha
iti uktvaa tat bilam shriimat praviveesha Svayamprabhaa.
CONTEXT: Hanuman and other Vaanaras coming out from the cave of Svayamprabha, while searching for Sita. Svayamprabha brings them out of the Cave after giving them food, rest and water. She informs them that they are at the Vindhya Hills.
ENGLISH GIST: Svayamprabha said: ‘This is "Vindhya" hill full of trees and creepers. This is "Prasravana" hill. This is the Sea. This is the great Ocean. Let auspicious things happen to you. Oh the best among the Vanaras, I am going to my residence.’ Saying thus, she went back to her cave.
CRITICAL REMARK: Vindhya Hills and the Ocean cannot be side by side. Absolutely impossible. Vindhya Hills do not have any sea shore.