This video discusses growing peppers and tomatoes by a suspended pot, non-circulating hydroponic method (commonly referred to as the Kratky Method) which does not require electrical power and pumps.

Here are some relevant articles;
Non-circulating hydroponic methods for growing tomatoes.
https://www.ctahr.hawaii.edu/hawaii/d...

Observations on a Non-circulating hydroponic system for tomato production.
https://www.ctahr.hawaii.edu/hawaii/d...

A suspended pot, non-circulating hydroponic method.
https://www.ctahr.hawaii.edu/hawaii/d...