I haven't been able to find much information on Indian or Chinese connections to Ptolemaic Egypt other than very general mentions of Silk Road trade and references to Ashoka sending missionaries to Alexandria. This would suggest that there was definitely contact between the civilizations but I'm curious if there is any more specific information available on the contact between these different ancient cultures. I'm particularly interested in the spread of ideas, especially medical knowledge (i.e. Hippocratic method vs Ayurvedic medicine) but any help would be much appreciated. Thanks in advance!
I'm not an expert in this field, but maybe I could just shed some basic understanding of the historical backdrop. From the 3rd century BC to around the year 0, you had in what is now Afghanistan and Pakistan the Graeco-Bactrian/Graeco-Indian Kingdom. These kingdoms were originally satrapies of the Seleucid Empire, but eventually split off. As you can imagine, as part of the Hellenistic world the kingdom was in good contact with the western parts of the Hellenistic world, at least until it was cut off from it by the expanding Parthian Empire in Iran.
There are accounts that a number of the later Greek kings, such as Menander I, converted to Buddhism, so it doesn't seem inconceivable that a portion of this Greek populace would have been aware of, or even converted to, Buddhism or Hinduism. these ideas would naturally permeate at some point back to the center of the Hellenistic world, Alexandria.