  We study the long Josephson junction (LJJ) model which takes into account the
second harmonic of the Fourier expansion of Josephson current. The sign of
second harmonic is important for many physical applications. The influence of
the sign and value of the second harmonic on the magnetic flux distributions is
investigated. At each step of numerical continuation in parameters of the
model, the corresponding nonlinear boundary problem is solved on the basis of
the continuous analog of Newton's method with the 4th order Numerov
discretization scheme. New solutions which do not exist in the traditional
model have been found. The influence of the second harmonic on stability of
magnetic flux distributions for main solutions is investigated.
