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Breaking integrability at the boundary: the sine-Gordon model with Robin boundary conditions

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Figure

Figure 1:(a) The scattered field after time evolution with initial soliton velocityv0 = 0.895 and boundary parameter k = 0.055.(b) The bound state eigenvalues,±0.146 + 0.288i, derived from the portion of the field between xL and xR in (a)
Figure 2:dashed line, 2�kink and antikink is returned from the boundary collision [5]
Figure 3: The graphical solution of Eq.(14) forthree critical values of k = 0.25 (solid line), and for the first k (dashed lines).
Figure 4: The energy,that if a pointwhile the solution found when approaching from the right contains a static antikinkuindicate the solutions of Eq.(14), which are also the stationary points ofenergy 8, soenergy contribution ofwith E, of a static antikink
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