  The particular type of four-kink multi-solitons (or quadrons) adiabatic
dynamics of the sine-Gordon equation in a model with two identical point
attracting impurities has been studied. This model can be used for describing
magnetization localized waves in multilayer ferromagnet. The quadrons structure
and properties has been numerically investigated. The cases of both large and
small distances between impurities has been viewed. The dependence of the
localized in impurity region nonlinear high-amplitude waves frequencies on the
distance between the impurities has been found. For an analytical description
of two bound localized on impurities nonlinear waves dynamics, using
perturbation theory, the system of differential equations for harmonic
oscillators with elastic link has been found. The analytical model
qualitatively describes the results of the sine-Gordon equation numerical
simulation.
