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Energy flow of moving dissipative topological solitons
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Image of FIG. 1.
FIG. 1.

Kink velocity as a function of the dc force for . Numerical solution of (22) , see the text for details (open circles) and approximative solution (26) (solid line). Inset: critical value from (23) for . Numerical solution (see text for details) (open circles) and approximative solution (25) (solid line).

Image of FIG. 2.
FIG. 2.

The densities of the scaled internal current, 0.02 (thin line), and of the exchange current, (bold line), for the , and . The region near the kink center at is zoomed.

Image of FIG. 3.
FIG. 3.

Space-time evolution of the soliton ratchet with the , , , , and : (a) Contour plot of the energy density (3) and (b) contour plot of the function defined in Eq. (50) . values are zoomed near the kink center.

Image of FIG. 4.
FIG. 4.

Numerically computed average values of the exchange current (lines) and total current (circles) as a function of the driving force parameter for (solid line, filled circles) and (dashed line, open circles). Other parameters are the same as in Fig. 3 .

Image of FIG. 5.
FIG. 5.

The internal (filled circles), the exchange (triangles) and the total (squares) energy currents as functions of the discretization parameter . (a) and (b): the case of the dc external force ; (c) and (d): the case of the biharmonic driving force (41) with and . for all cases. The dash-dotted line in (b) indicates the exchange current value, , calculated for the continuum limit within the pendulum approach (see Table I ). The dashed line in (c) corresponds to the power-law asymptotic .


Generic image for table
Table I.

The values of the internal, exchange and total currents for the damping constant and an infinite system size , calculated within the pendulum approach for . and are the errors of the calculated internal current and the accuracy at which the current balance relation (16) is fulfilled, respectively (see the main body text for details).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Energy flow of moving dissipative topological solitons