Hello revtim,
Sounds like one cylinder not producing power.
A quick check is with a spray bottle to see if water burns off of each exhaust outlet rapidly. If one does not, you found the none working cylinder.
Simple is the best approach: Start by replacing the plugs.
Next would be a possible coil failure. There are many You tube videos that can help replacing one a setting the proper air gap.
If the upper engine cover has never been off for a good cleaning, overheating of the cylinders and a failed head gasket are a real possibility.
Here is a parts source according to your engine number
Find genuine OEM replacement parts and diagrams for the *SHORT BLOCK ASSEMBLY for the Kawasaki FX801V-FS04 - Kawasaki Engine
www.partstree.com
Keep us posted on what you find, because many of us can easily write a lot about "what it could be" but let's take it a step at a time with the diagnostics first.