Jet engines can run on almost any fuel, and the operating temperatures of modern jet engines' hottest sections are anywhere between 3000 and 3150 degrees F (1648 and 1732 degrees Celsius). Does that mean that a hydrogen on-demand system could work on modern jets?
Water is pumped and heated first by the exhaust section, then directed towards the hotter sections of the engine (when hot enough to not cause cooling and lower engine efficiency) where it's broken down into hydrogen and oxygen at a heat above 1472 degrees F (800 degrees Celsius), then those gases are pumped into the engine for combustion.
The advantages are that firstly, water is abundant and therefore cheap. Even sea water could be used because at those temperatures it's easy to design a system that would get rid of the impurities that would otherwise corrode critical engine parts.
Secondly, it would save on manufacturing costs given that non-heat critical parts in the exhaust section would not need to be made of sophisticated and expensive materials and alloys given the cooling effect of water.
Thirdly, the costs of the fuel weight would be reduced given that the energy density of hydrogen is twice that of fossil fuels, so less would need to be carried. And most importantly, the environment problem would be solved in aviation given that there would be little or no carbon dioxide emissions.