It is commonly claimed in Nyaya and Vedanta circles that Udayanacharya brought an end to the long-standing philosophical debate between Buddhist thinkers and Vaidika traditions. His works, such as Kusumanjali, Atmatattva Viveka, and Nyaya Vartika Tatparya Parishuddhi, are said to have decisively refuted core Buddhist doctrines like shunyavada, kshanikavada, and vigyanavada.
A Traditionalist Vedantin author summarizes this viewpoint as follows:
**"Dharmkirti who is well known for his scholarly works, criticized nyaya doctrines and Vartikam in his Work called “Praman -Vartika”. After Dharmkirti Buddhism went into decline, last work which was a considerable criticism was written by a Nalanda professor as “TatvaSangraha”. In This tatvaSangraha the writer had also tried to critize BhagvatPad Sankara’ views (verse 330-331).
Vachaspati misra who was the knower of 12 darshanas, He wrote Nyaya Vartika Tatparya tika and answered the claims that were made till now in a very good manner. His refutations are Calm,deep and subtle.**
An unexpected refutation came from Kashmir and that was from Jayanta Bhatt. He wrote an independant commentary on NyayA suTras called “Nyaya Manjari” He established the authority of the Veda and refuted the buddhist doctrines mercilessly. He has quoted everyone be it DharmaKirti, Dingnaga or Dharmottara.
Bhasvarajna an other Kashmiri wrote ‘NyayaBhusana’. He criticized everyone from Nagarjuna till Prajnakara Gupta(writer of VartikaAlankara).
Jayanta Has wrote a verse while refuting ????????? which goes as follows :-
???????????? ???????????? ? ???????? ??????????? , ????????? ???????? ?????????????????? ??????? ????? ? ???? ????????? ????? ????? ?????? ?????????, ????????? ????? ??????????? ??????? ????? ??? ?
You Bauddhas, hold that there is no soul, yet you construct caityas (towers) to enjoy pleasure in paradise after death; you say that everything is momentary, yet you build monasteries with the hope that they will last for centuries; and you say that the world is void, yet you teach that wealth should be given to spiritual guides. What a strange character the Bauddhas possess; they are verily a monument of conceit.
JnanaSariMitra and his disciple RatnaKirti wrote some works answering Vachaspati and made last tries to save buddhist philosophy from the attacks of logicians.
UdayanaCharya ended this debate with very strong logics. He composed works as “Kusumanajali” “Atma Tatva Viveka” and “Nyaya Vartika Tatparya Parishuddhi” and refuted ShunyaVada,KshanikVada,VigyanVada.
There are other works as Bauddha Dhikkara tika(sankara misra) and Bauddh dhikkar shiromani but till then Buddhism became a history."
Source - The Literary debates between Buddhists and Vaidikas
Given this narrative, my question is the following:
Did any later Buddhist philosophers, either in India, Tibet, Nepal, or elsewhere, directly or indirectly respond to Udayanacharya's arguments? Are there surviving texts or commentaries that attempt to refute or answer his critiques of the Buddhist doctrines of no-self, momentariness, and emptiness?
Or did the Buddhist tradition leave Udayana's works unanswered, either due to historical decline or strategic neglect?
Any textual, historical, or scholastic leads would be much appreciated.