I've got a couple of induction stove tops. They mostly use 2kw max, but pulse on and off to emulate lower power levels. So if you can't supply 2kw, you'll not have a good time.
I have run one on a 2kW inverter and an AGM battery.
https://www.ikea.com/au/en/p/tillreda-portable-induction-hob-1-zone-white-40493509/
They are dirt cheap, so not a huge risk if it doesn't work.
