Not compatible with the output. Get a plain jane radiant portable burner, or use the grill.

To investigate this further would require measuring the generator waveform (voltage, frequency, and shape), and the start-up current draw of the cooktop. Your cooktop may be finicky about what its power source looks like in waveform and source impedance. My former Kenmore and current Frigidaire induction cooktops (Electrolux designs) run happily from my 20 kW Milbank fixed motor generator, along with other concurrent household power loads.

From the point of view of emergency use of your induction cooktop, the simplest method of addressing it, excluding the good suggestions of @User, would be to obtain a sine wave output UPS that can do 240 Vac at the needed current load of your cooktop. This would be somewhat expensive, but significantly less than the purchase and installation costs of a propane tank and motor generator/auto transfer switch setup that had relatively clean output. Battery replacement every 5 years should be incorporated in the cost-benefit analysis.

Fiddly high end electronics are picky about what they get.

For infrequent emergency use, I'd just get an alternative like Verbo suggests. The nice thing about induction is that even if it isn't running, it still makes a good surface to park a camp stove under the hood which doesn't object to a generator. :)

kaseki kind of nailed the answer here. Most generators put out a chopped or stepped sinewave and induction electronics don't play well with them.

We get occasional power outages of up to a week & have a portable generator. My old electric skillet comes in handy.

Thanks, everyone. We do have a double burner smooth top on the lower level. It worked fine, so we can use that if needed.

I would love to have a standby generator. We have a 500 gallon propane tank for a few things and it would probably be sufficient for occasional outages.

The suitability of a propane tank depends on the minimum temperature of the soil (if buried) or air and the rate of liquid propane that must evaporate from the liquid surface area (at 85% fill) for the motor/generator to be powered. There are tables for this. I have a buried 500 gal tank here in southern New Hampshire and it works fine for my 20 kW generator. Mine tests itself every week and runs for 20 minutes, so I can take notice if there is any problem when it is cold. The starting battery should be changed roughly every 3 or so years in cold climates. A weak battery will reveal itself in a snow storm.

We put in a standby generator when we bought this house but we opted not to service the induction cooktop or any ovens with it, in part because the existing underground propane tank was small. So we get out the old Breville oven, and I invested in a $19.99 hotplate from Walmart. Works for us