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Dynamics of kinks of the modified sine-Gordon equation in the presence of stepped spatial modulation of the periodic potential

Keywords:

E.G. Ekomasov, R.R. Murtazin, O.B. Bogomazova


In this work, dynamics of kinks of the sine-Gordon equation in mediums with stepped spatial modulation of the periodic potential (or in mediums with a defect) has been studied analytically and numerically. For the case of kink motion by inertia, the equation of motion for the center kink, and the value minimum velocity of kink, which necessary for overcoming the defect, and the dependence of the limiting velocity of kink motion after passing of the defect from the initial velocity has been found analytically, using the perturbation theory of solitons. For the case of the motion kink permanently under the external force, changing the structure of kink, and the dependence of the minimum velocity and the limiting velocity of kink motion from the external force has been determined numerically. It was shown that for the case of small defect, the analytical and numerical results coincide well. For the case of pinning of kink in the region of the defect, the dependence of the frequencies of exciting the internal modes of kink translating and pulsating types from the external force has been determined.
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