Buddha mentioned in Gita Govinda as Avatar of Vishnu and Gautama Buddha, founder of Buddhism--are they the same?

 Buddha mentioned in Gita Govinda as Avatar of Vishnu and Gautama Buddha, founder of Buddhism--are they the same?

In fact, is it Gautama the Buddha in Gita Govinda?

Accepting that it is for arguments sake, we have to view all the descriptions from a historical perspective also.

.Jayadevan’s Lifetime is stated to be the twelfth century(second half) A D.. We can safely presume that the identify of Buddhism as a separate religion has been lost for all practical purposes in India, and we have to remember that Jayadeva essentially belongs to Orissa which is the Kalinga Desam of old, which Ashoka the great conquered in the first or second century BC.. And he embraced to the way of Buddhism after the Kalinga War. So Buddhism must, and has taken roots.. And with the local Hinduism gaining ascendency, even the votaries of Buddhism would have crossed over back to Hindu practices.. And Jayadeva is a poet and his wife Padmavathi is a dance artists.. He was patronised by the local ruler who was also engaged in Krishna worship,, Anyway Jayadeva was not getting Brahmin patronage, and was not a major votary of Vedas.. And the re-entrants from Buddhism could get re-entry into the highest echelons of Hinduism with Vedas as the rallying point... In fact the idol worship of temples depended on the Tantras and local spell and charms, more than on Vedas.. And the Vajrayana school of Buddhism especially present in the east along with Durga, kaali worship of Bengal and below all Indicate that the religious practice prevalent in the era of Jayadeva did not have much to do with Vedic ascendancy.. This parallel religious movement could have something to do with the Bhakti movement in India... actually a splinter group of Hinduism like sufism and Islam..Chaitanya Mahaprabhu also is a product .of such a deviation and so also the Krishna movement.. Therefore, putting legends and faiths of the time together, they placed Buddha, who was nothing but a rebel from Hinduism in the 3rd century BC.too in the pantheon of the ten Avatars of Vishnu.. Dissent from Vedas was not a big issue, and the votaries of Bhakti cult actually did not care much about Vedas.. If we can put all these things together, the entry of iconoclast Buddha as a Hindu avatar can be understood..

Hinduism is often a mixture of so many traditions and practices.. Pro-Vedic and anti-Vedic schools are present.. We have to view things in this perspective.. For Vedic Brahmins Vedas is the ultimate. However, for many other Hindus, Veda was a neutrality. They could praise the Vedas in one verse and criticize them in another.. Perhaps this has happened in the Dashaavataaram description of Gitagovindam too..

For me Krishna is a symbol of Mysticism, Symbol of spirituality, and not of Vedic or puranic epoch, essentially..

Hinduism is ready ever to accept all great ideas..and Vedic Hinduism os only a part of that huge ocean of catholicity