Dr Coshan, 75, disappeared from the Seafield Road area of Edinburgh on August 11 before midnight and was reported missing the following day.
The body was found on land close to the A696 near the village of Kirkwhelpington on Sunday September 4.
Specialist officers were seen close to scene combing woodland more than 80 miles away from his home in Edinburgh.
His family has been made aware and specialist officers are continuing to provide support to them.
Two men, aged 27 and 63, have previously been arrested and charged in connection with Dr Coshan’s death.
Detective Superintendent Andrew Patrick, of Police Scotland’s Major Investigation Team, said: “Our thoughts remain with Peter’s family at this incredibly difficult time.
“I would again like to thank everyone who has come forward with information which has helped our investigation.”