Critical relations in symmetric $0-\pi$ Josephson junctions

Numerical modeling of dependences ``critical current -- external magnetic field'' for geometrically symmetric $0-\pi$ Josephson junctions is performed. The calculation of critical current is reduced to non-linear eigenvalue problem. The critical curve of the contact is obtained as an envelope of the bifurcation curves of different distributions of the magnetic flux. The structure of vortices in contact is observed explicitly and the dependence of the basic physical characteristics of these vortices on junction's length is explored. The comparison of numerical results and known experimental data shows good qualitative and quantitative conformity.