Unfortunately, the best source we have is a Roman source from the period. The best historian of Trajan's reign was Cassius Dio (book 68.17-33), who wrote about the Parthian wars. His account is problematic as it refers to the Parthians in function of the Romans, not as an independent power in its own right. Apparently Arrian wrote about Trajan's campaign in his work titles the Parthika, but we only have a rough Byzantine summary of it by the scholar Photios.

If you wish to learn more about the Parthians from primary sources, I would recommend Justin's Epitome of Pompeius Trogus.

Here are some links: http://www.shsu.edu/~his_ncp/Parthian.html

http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Cassius_Dio/68*.html