British transport police are looking for witnesses after the incident that took place at the 20.32 service from Edinburgh Waverley on Friday 22 October.
A woman aboard this train noticed a man staring and waving at her.
He then sat down next to her and began making sexual remarks to her before sexually assaulting her.
The man is described as a black man or medium build, about 6 feet tall and with a scar over his eyebrow.
He was wearing a navy blue Moncler jacket, black jeans and blue and white trainers.
Witnesses or others with information can contact the UK Transport Police by texting 61016.
You can all call them on 0800 40 50 40 with reference 705 of 22/10/21.
Alternatively, you can call Crimestoppers anonymously on 0800 555 111.
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