No... and yes. :-)
Others (Congress and/or the president) get to determine when they are over... but the Supreme Court gets to interpret whether they've said that or not.
As an example. Only Congress has the power to declare war", but the courts have long ruled (correctly) that when congress authorizes hostilities and pays for the combat, that the fact they never used the phrase "1,2,3,4 we declare war" is irrelevant.
I don't know about "irrelevant", just not applicable to the President's powers to wage a war. There are a number of provisions of law that are only activated under a declared war(such as enhanced punishments, and suspensions of rights), and I don't think they've been tested.