Could you tell me how to write the following surface integral in Maple, please?

Why is there a difference between pdetest and algsubs for a PDE?
Shouldn't pdetest work the same as algsubs for the example below?

restart: with(PDEtools):

Eq:=u(x,t)*diff(u(x,t),t)=0:

tmp:=sin(w*(c*t-x))-(1/4)*epsilon*c^2*cos(w*(c*t+x))^2+epsilon*c^3*w*cos(w*(c*t-x))*sin(w*(c*t-x))*t+(1/4)*epsilon*c^2*cos(w*(c*t-x))^2+(1/8)*c^4*epsilon^2*sin(w*c*t+w*x)+(1/8)*c^4*epsilon^2*sin(w*c*t+w*x)+(1/24)*c^4*epsilon^2*sin(3*w*c*t+3*w*x):

sol:=u(x,t)=tmp: