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The particular type of four-kink multi-solitons (or quadrons) adiabaticdynamics of the sine-Gordon equation in a model with two identical pointattracting impurities has been studied. This model can be used for describingmagnetization localized waves in multilayer ferromagnet. The quadrons structureand properties has been numerically investigated. The cases of both large andsmall distances between impurities has been viewed. The dependence of thelocalized in impurity region nonlinear high-amplitude waves frequencies on thedistance between the impurities has been found. For an analytical descriptionof two bound localized on impurities nonlinear waves dynamics, usingperturbation theory, the system of differential equations for harmonicoscillators with elastic link has been found. The analytical modelqualitatively describes the results of the sine-Gordon equation numericalsimulation.

Dynamics of the multi-soliton waves in the sine-Gordon model with two identical point impurities