D-lines in superconductor with triangular defect

Steady currents in a superconductor film show a surprising phenomenon, the discontinuity lines. If there are cracks or indentations in the film border, perturbations appear in the current flow that span large areas, even of infinite extent in the case of a perfect superconductor in the critical state. The simple Bean model predicts that the perturbation corresponds to real discontinuities in the current direction, the d-line, and with parabolic shape starting from some distance of the indentation. Later, more detailed and accurate work by Gurevich showed that the d-line due to a planar indentation is actually parabolic in shape far from the indentation, but a slightly different factor of the one obtained with the Bean model. The Bean model also predicts that the d-lines produced by a triangular indentation of the same height as a planar indentation will produce also the same parabola at some point.
This is proved also with Gurevich's hodograph method in my work: Calculation of currents around a triangular indentation by the hodograph method, https://arxiv.org/abs/1812.10798v2.
A nice mathematical relationship I stumbled upon for the demonstration is the following expression for the Kronecker delta, obtained from Fourier series expansions of different parity: 

Here some of the current streamlines and magnetic field lines for a semi-infinite film: