How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax.

    κ=0.2; xmax=10;

    eq1={1/κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3};
    eq2={a''[x] == a[x] f[x]^2};
    boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};

An attempt to use NDSolve with the shooting method didn't work.