Just for safety sake lets not get confused with "tire shake" and the "death wobble" trust me, I'll take a tire shake any day compared to the wobble.
I have had it happen to me three times, ALL in a straight line, All over 100 mph. In my opinion the best way to get the bike back under control, and how I handled it each time, is to apply the brakes as firmly as you can slowing down as quickly as the situation will allow. This is obviously only my opinion and what worked for me. When this happens, espespecially the first time, it will scare the living crap out of you, speeding up isn't going to compute in your brain in that second of panic.
I have had it happen on two "brand new" bikes, 05 Fat Boy and a GSX 750 Suzuki. Let me clearify......... new enough that tire wear did not come into play. The third was an older Kawasaki I can't remember the model but it was built to the hilt and very very fast for the times. This one was the worst and I almost crashed at over 120.
I think there are many factors that can come into play and I think the startng point of each is the frame. Then you add in wheel type, windshield, floor boards, fender types, whats mounted on one side and not the other, WHAT IS MOUNTED MORE FORWARD ON ONE SIDE THAN THE OTHER. The other main factor, in my opinion, coupled with these other factors, is the force of acceleration and the direction it attempts to move the machine. While under acceleration and even when traveling at a high rate of speed, every bike, allthough sometimes very little, the engine force will push to one side, to the left or to the right. When you factor in the other conditions this will have an impact. On a Harley, I have not researched this and is only my theory, I would bet that the wobbles that occure in a sweeping corner are specific to right or left side drives. I know of numerous 90+ wobbles on sporty's that only happened in sweeping corners and all the same direction.
No chithead or xpert titles please!!