There are some wetlands in our subdivision which are overrun with phragmites. Some of these have established themselves in our neighbor's backyard and now they're spreading throughout our lawn.
I've tried pulling a couple of them out, but they have these hefty runners under the ground and pulling them out (when possible at all) totally rips up the lawn.
This is our backyard. You can see the phragmites peeking over the top of the fence and shooting up in our lawn.
Here is a closer view.
What is the best way to get rid of these? The only thing I can think of is to mow them down (again) and apply an herbicide (RoundUp? Rodeo?) directly to the stems with a sponge brush or dropper so I don't kill the grass, and possibly to try to put a barrier along the fence (which would probably involve trashing the lawn).
As an additional complication, our yard appears to be poorly graded, so that corner of the yard is constantly soggy, which I'm sure the reeds love.
Does anyone have suggestions? How can I get rid of these?