Induction cooktops use HUGE power - one I installed at a friends house needed 30amps total. That's over 7KW - and as mentioned, the power factor is horrendeous so without a pan on the stovetop there's a lot of VAR's to consider too. Even with one plate running you'd need ennormous battery bank to cook a meal. The ebay jobby shown uses 2KW for one plate - remember you'll need it for at least half an hour or so to cook a meal. That's over 160 amps continuous from your batteries - the cabling would need to be pretty good too.
Infrared are a little better but still huge power draw and unfortunately unrealistic to run off batteries and an inverter. Love it or hate it, gas is the only economical way of having a decent cooktop. You could use a Coleman dual fuel stove, but if carrying flamable stuff around bothers you, that's no good either.
Could run a genset while you're cooking and do it ok though.

