No - solarization won't work. How much have you got? If it's a lot you can look forward to thrice yearly application of something nasty over three years minimum. That's what I endured and there's still a bit left.

If it's one clump you could dig it out but dig very deep and very wide. This stuff is the most hellish plant in the universe if it's where you don't want it imo.

I've managed to eradicate about 90% of my infestation with a combination of concentrated roundup applied to newly-cut surfaces (when it was large, having been left to us by the former owners of the house), and lots and lots of digging up sprouts over the past three summers. Each year it seems a bit more enfeebled, and I seem to be winning...slowly.

Keep in mind that the World Health Organization has stated that glyphosate products are carcinogens, cancer causers.

kimmq is kimmsr

We know that kimmsr - believe me I didn't like using it. In fact I didn't. I got a professional team in who specialise in Knotweed eradication and do the job in full protective gear. JK is that serious a problem here. It's the only time in decades of growing stuff that I have ever resorted to Glyphosate. But the JK was destroying the biodiversity of my ancient broadleaf woodland bit by bit. Biological controls are being researched as a matter of urgency because we know chemicals are not the long term answer. But at present it's all we have. http://www.cabi.org/japaneseknotweedalliance/why-is-it-a-problem/