So as I`m gathering, the story behind the waves is this... Uhumm...
There are 2 worlds... Middle Ages and Japanese... They both get waves of monsters from another dimension, but only one at a time. So if one world has a wave open the other doesn't.
Medieval world fights the waves, but Japan world figures out the condition and chooses to makes the waves stay at the other world.
"if it's happening to you then it's not happening to me".
They heroes travel to the world stop, or kill, anything that could stop the waves.
Something like that?