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

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