Well my guess is that E is the total energy and P total momentum of the wave, you can check for units if they are the same ones as they should be, anyway that's my guess.
LetE:=1/2(Tyxx+ ½ytt ) and P := Tyxyt.
Show thatEt = Px and TEx = ½Pt
and deduce thatE and P are also solutions of the wave equation, i.e.
TExx = ½Ett and TPxx = ½Ptt.
What are the physical interpretations ofE and P?
I am unsure of this, the physical interpretation of E and P.. are they the nodes?