Are there Indian accounts of the Battle of the Hydaspes River?
If so, what are they, who authored them, and how do they differ from the Greek & Roman accounts?
There are no Indian accounts of the Battle of the Hydaspes River.
It is difficult to prove a negative, but since there is very little historical material from that era (326 BCE) at all, we can be reasonably certain that there are no historical accounts. Tarn (1966) discusses this when talking about the Bactrian Greeks.
Had the story of the Bactrian Greeks survived, it would be considered one of the most remarkable of a remarkable time; but though it was treated by two Greek historians of the Farther East (Chap. II), nothing has come down to us directly but some fragments and scattered notices and the coins. And there is not even the help which can be got in Indian from Indian literature and inscriptions and from archaeological research...
The Bactrian Greeks weren't exactly the same area and time as the battle, but this quote points to the paucity of evidence during the era. Schmitthenner (whom I was referred to by this interesting article on Ancient Indian sources) has a strong opinion on ancient Indian historiography.
It is common knowledge that there is no corresponding equivalent on the Indian side. Ancient India has no historiography in the European sense of the word—in this respect the only 'historiographic civilizations' of the world are the Graeco-Roman and Chinese ones—and the 'Chronicles' of Ceylon, strongly imbued with religious tendencies, are no exception, in spite of Paranavitana's hypothesis regarding their scope in retrospect.
The closest Indian source we have to the period is the "Arthashastra" by Kautilya, who some identify as Chandragupta Maurya's (340 BCE – 298 BCE) minister. To be clear, the Battle of the Hydaspes River is not mentioned in this work; I only point it out because it is a rare example of writing near the relevant period.
It is worthwhile to note that even the Greek accounts of the battle are secondary: Arrian wrote his account hundreds of years after the fact, albeit he used sources (now lost) that were written closer to the time of the battle. Unfortunately, it seems that Greeks are the only source of information on this battle.
William Woodthorpe Tarn. The Greeks in Bactria and India (1966).
Walter Schmitthenner. Rome and India: Aspects of Universal History during the Principate. The Journal of Roman Studies, Vol. 69 (1979), pp. 90-106.
I request the reader to understand that in my writing I do not mean blemishing any religion. I am just putting the historical facts together without any prejudices.
It is quite likely that there would be no literature available in India to support or oppose any claims regarding the battle of Hydespas because this region near the Beas river has been a constant war-zone since the 10th century. The Takshshila University (situated in king Ambhi's kingdom), the most famous University of those times was in close vicinity to Porus's kingdom. This University and the other seats of learning nearby were been burnt to ashes during the Afghan and the Mongol invasions. The warfare of those times, especially in that part of the world, involved razing to ground the entire city or the town by looting it and then by burning down everything.
The north-western areas of ancient India (modern day Pakistan) and Northern India have witnessed many of these barbaric invasions after the 9th century as Afghan invaders frequently invaded these areas. It must be remembered that most of the learning centres in India were full of Hindu or Buddhist or Jain literature and studies. They, like many religious sites, were specifically targeted and burned down by the invaders who were followers of Islam. Nalanda University in ancient Magadha was also not spared. So it is probably not going to be possible to find any account of such an ancient battle.