A new rug may have waves or ripples in it when it s first unrolled.
How to get ripples out of a rug.
Again use a low heat setting when aiming your blow dryer toward the rug to avoid burning or melting the fibers.
What has worked for me is flipping the entire rug over and putting something heavy on the ripple.
As a last resort hire a professional rug cleaning company to steam the rug with a steamer or truck mount and dry it on an air table.
Always hold the hair dryer 6 to 9 inches away from the rug and use a sweeping motion.
Use the ice cube method for furniture dents.
Ends may curl up and the rug may get out of square easily.
Pry the carpet gently up from the strips with a wood chisel or other pry tool on a wall parallel to the ripple.
However the ripples may recur when moisture is again present.
Smooth it as flat as you can and allow it to rest for a day or so.
The fibers will relax on their own.
Using a comb and a blow dryer gently brush out rug wrinkles.
Pull tacks with a carpet tack puller a small metal claw on a short thick shank or.
The problem is you have to leave it like that for days but there seems to be no other way to work it out.
For these rugs if moisture is the problem the situation can sometimes be corrected by wetting the backing and tacking the rug out in a stretched position.
Direct sunlight for several hours should help the rug release tension naturally and at the very least make it more supple for reverse rolling as noted in suggestion 1.
If the dent is deep you can mist it with clean water in a spray bottle first to help the fibers relax.
Regain that spring in your step and your carpet by making a beeline for the bath to collect a blow dryer and spray bottle filled with water.