Hi...

I need to solve the pde 

eq := diff(diff(V(y, t), y, y)-alpha^2*V(y, t), t) = -I*alpha*U(y)*(diff(V(y, t), y, y)-alpha^2*V(y, t))-I*alpha*(diff(U(y), y, y))*V(y, t)-(diff(V(y, t), y, y))+alpha^2*V(y, t)

with U(y) as a known function

and boundary conditions as

bcs := {V(-1, t) = 0, V(1, t) = 0, (D[1](V))(-1, t) = 0, (D[1](V))(1, t) = 0}

and initial condition as

V(y,0)=phi(y);

both of phi(y) and U(y) can...