[ariel]

It is an interesting and complicated question. My guess it is not either/or but a combination of both .

Simplifying things a bit, one can say that all sword blades can be put into four different boxes: straight, curved, recurved and wavy. Thus, it would probably be inevitable that totally separate societies might produce identical forms without any actual knowledge of the each other’s existence: purely parallel development.
My guess is that the Ancient Greek kopis and Indian Nair swords fall into this category. Another similar but later example would be Central European Bauernwehr ( Kord) and Afghani Khyber knife.

However, Indo-Muslim Sossun Pata may indeed stem from the Ottoman yataghan. I have already shown here an almost certainly original “ marriage” of a Tulwar handle and a genuine Ottoman yataghan blade. Turkish janissaries served as mercenaries in Indian armies. Deccan sailaba is another example: Some Deccan sultanate were established and led by the emigrating Turks.