It doesn't matter which Knotweed it is, the eradication is the same: DIG! Dig up the plants, dig up the rhizomes, follow the runners and dig them up. Whenever a new one pops up, dig it up and follow the runners to the source (they can travel 50 or 60 feet). If a plant you want to keep is in the way, dig it up too (you can replant it after you have followed that runner).
You might be able to kill it with brush killer in the fall. Just as the leaves start to yellow, the roots are pulling nutrients down at an accelerated rate in preparation for surviving the winter. Spraying brush killer (at almost full strength) can do major damage to the plants. But it will also do major damage to any other susceptible plant nearby and it (unlike Roundup) does sink into the ground with some residual effects, especially in wet areas.
If you can cut them down to a couple inches and paint the stumps with full strength Brush Killer, it will help.
Good Luck!
