With respect to the attack by the irredentists of the former Islamic Caliphate called "The Ottoman Empire", they declared war on us. Until they surrender and sue for a peace treaty we are at war with them.
The Constitution clearly establishes the fact that the President has an open ended right to repel invaders. "W" bothered getting an authorization to use force though.
Again unless you can come up with some Constitutionally prescribed piece of wording that says "Declaration of War" you will have to live with what the Constitution says on the matter.
Now, regarding peace, presumably the President can make a treaty with just about anybody ~ country or otherwise ~ and with 2/3 concurrence of the Senators present and voting, that becomes law.
In short, the President can stop fighting a war if and only if he has the concurrence of the Senate with a super majority. To that degree the Constitution has a clear BIAS toward continuing war ~ once engaged ~ which is something you should really think about. Not only do we give the President the authority to defend the nation once he starts doing that he's on the hook until a super majority in the Senate says he can stop taking those actions.
Currently that would include making war against any forces of any kind in any part of the Former Islamic Caliphate!
And just because a few hijackers "declared war on us," as you put it, that doesn't constitute a declaration of war by our government. It has to be bilateral, and it has to be a formal declaration.
The Constitution clearly establishes the fact that the President has an open ended right to repel invaders
Repelling invaders is not the same as declaring war on the country they came from.