Hi.. I don't have experience with your application but have in sizing and using industrial generators starting and running large industrial plant. (principals are same)
The other comments from B40-Lefkas are very valid too.
From a electrical point of view.
Generators need to sized to suit the greatest starting load they will experience in this case 36.5A + A factor for duty cycle
A 2kw or even 2.2kw generator is simply not big enough to be a long term reliable solution - you may get away with it working for a while but you'll over load the generator every time it starts or restarts.
You don't mention the running current so I cant calc the generator size required - you can plug your numbers in to these two web calculators.
see this online calculator and motor data
http://www.dieselserviceandsupply.com/Power_Calculator.aspxhttps://www.rm-electrical.com/technical/motor-motor-current-charts/ (from US web sites)
from your info
115v at 35.6A = 3.32kw.
its the starting current (35.6A) that need to get the loading running, but once its running needs a lot less power to keep it running.
The 15A circuit breaker would be a 'type C' which is designed to allow for higher startup motor currents for a short time.
the suggested 15A is the overload current rating (ie normal running current protection).
I hope this helps