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Decay of bound states in a sine Gordon equation with double well potentials

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Figure

FIG. 1. Time-dynamics of the system’s bound states for athe same amplitude. Elevation plot of = 1 and L = 2, when both modes are excited initially with relatively φ(x, t).
FIG. 2. Oscillation amplitude of the breathing coupled modes. The case λ2 > λ1 > 1/3, with no driving (h = 0)
FIG. 4. The same time-dynamics of the system’s bound states as in Fig. 1slowly increasing in time to, but with nonvanishing drive amplitude, that is h = 0.03.
FIG. 6. The same as in Figure 3(a), but for nonzero driving amplitude. The panels correspond to h = 0.006 and h = 0.008.Analytical approximations (91) and (92) are shown as green and blue lines (in both panels, the larger amplitude oscillatorycurve corresponds to the asymptotic solution of A1, the smaller amplitude curve to the numerical simulation of A1, the lowestcurve shows the asymptotic solution of A2, whilst the upper decaying curve illustrates the numerical solution of A2).

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