A vectorial function $\boldsymbol{f}(\boldsymbol{x})$, satisfies the following PDE
$$ (\boldsymbol{c \cdot \nabla}) \boldsymbol{f}(\boldsymbol{x}) = \boldsymbol{A}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{x}). $$
The vector $\boldsymbol{c}$ is constant, and $\boldsymbol{A}(\boldsymbol{x})$ is periodic in each of its arguments, i.e. $\boldsymbol{A}(x_1, \dots, x_i, \dots, x_n) = \boldsymbol{A}(x_1, \dots, x_i+2\pi, \dots, x_n)$.
Which boundary conditions should I impose in order to numerically find one of its fundamental solution matrices?