Russia still has 10k nuclear warheads!
The russians can make the Caucasus inhospitable for NO ONE for the next 10000 years.
Putin, your move.
Don't forget about Armenia. They're Christians who have suffered multiple genocide at the hands of Ottoman Turks (Muslims) during the early part of this century. We don't want to make Armenia uninhabitable.
Nuclear warheads also produce dangerous radioactive fallout which will drift thousands of miles from the detonation area; therefore, they are not the answer.
My best guess: Call for UNITED STATES SPECIAL FORCES allied with ISRAELI DEFENSE FORCES to root out terrorists and train and equip the hapless Russians to do the same. At this point, the Russians will not suffer defeat for failure of the will.
Probably not necessary to go that far but it will be interesting to see what Putin's next move will be.
What he should do is join W in the war on terror but I'm assuming that won't happen.
So, based on that assumption, what I would do if I were Putin is:
1..Pick the town that most likely is the origin of the terrorists.
2..Round up ALL the muslim children and make them wards of the state.
3..Round up all the muslim women and relocate them to other towns.
4..Round up all the muslim men and send them to Siberia to never be heard from again.