Influence of Josephson current second harmonic on stability of magnetic flux in long junctions

We study the long Josephson junction (LJJ) model which takes into account the second harmonic of the Fourier expansion of Josephson current. The dependence of the static magnetic flux distributions on parameters of the model are investigated numerically. Stability of the static solutions is checked by the sign of the smallest eigenvalue of the associated Sturm-Liouville problem. New solutions which do not exist in the traditional model, have been found. Investigation of the influence of second harmonic on the stability of magnetic flux distributions for main solutions is performed.