# Problem in implementing periodic boundary condition to solve a system of PDEs with period 2 Pi/constant

I wish to solve the following system of PDEs for h1, h2 using periodic boundary conditions and specified initial conditions. When I execute Mathematica complains that the boundary conditions are not consistent

    System1 = {D[h1[x, t], t] == -D[Q1[x, t], x],
D[h2[x, t], t] == -D[Q1[x, t], x] - D[Q2[x, t], x],
h1[x, 0] ==
0.5 + A0*h1L*Exp[Sqrt[-1]*alpL*x] + B0*h1S*Exp[Sqrt[-1]*alpS*x],
h2[x, 0] ==
1 + A0*h2L*Exp[Sqrt[-1]*alpL*x] + B0*h2S*Exp[Sqrt[-1]*alpS*x],
h1[-40, t] == h1[40, t], h2[-40, t] == h2[40, t]}


I also tried it with PeriodicBoundaryCondition function but it gives "Equation or list of equations expected instead of h1[x,t] in the first argument {h1[x,t],h2[x,t]}".

System = {D[h1[x, t], t] == -D[Q1[x, t], x],
D[h2[x, t], t] == -D[Q1[x, t], x] - D[Q2[x, t], x],
h1[x, 0] ==
0.5 + A0*h1L*Exp[Sqrt[-1]*alpL*x] + B0*h1S*Exp[Sqrt[-1]*alpS*x],
h2[x, 0] ==
1 + A0*h2L*Exp[Sqrt[-1]*alpL*x] + B0*h2S*Exp[Sqrt[-1]*alpS*x],
PeriodicBoundaryCondition[{h1[x, t], h2[x, t]}, x == 2*Pi/alpL,
Function[x, x - 2*Pi/alpL]]}


The constants and the expressions are provided in the attached .nb files. Kindly help!