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/downloads/Non-Circulating_Hydroponic_methods_for_growing_tomatoes.pdf

Observations on a Non-circulating hydroponic system for tomato production.
https://www.ctahr.hawaii.edu/hawaii/downloads/Observations%20on%20a%20Noncirculating%20Hydroponic%20System%20for%20Tomato%20Production.pdf
A suspended pot, non-circulating hydroponic method.
https://www.ctahr.hawaii.edu/hawaii/downloads/A_Suspended_Pot_Non-circulating_Hydroponic_Method.pdf
Grow Kratky
