Kink velocity in nonstationary external fields for the sine-Gordon model with allowance for dissipation effects

With the help of energy analysis suggested by McLaughlin and Scott for the sine-Gordon equation, evolution of kink velocity modeling the propagation of a local conformational perturbation along the DNA molecule under the simultaneous action of dissipation effects and special nonstationary external fields is investigated. For a harmonically time-dependent external force, the kink velocity is characterized by oscillations about a rather monotonically decreasing trend expressed by an explicit analytical formula. The trend velocity coincides with the results of calculations of the kink velocity averaged over the period on different time intervals. Similar results are obtained for a nonstationary force in the form of a step function. A numerical analysis, in particular, demonstrates that the trend velocity changes its behavior for certain values of rectangular pulse duration.