Remarks on sine-Gordon kink–fermion system: localized modes and scattering

Comment on "Existence of internal modes of sine-Gordon kinks".

In Phys. Rev. B 42, 2290 (1990) we used a rigorous projection operator collective variable formalism for nonlinear Klein-Gordon equations to prove the continuum sine-Gordon (SG) equation has a long lived quasimode whose frequency is in the continuum just above the lower phonon band edge with a lifetime . We confirmed the analytic calculations by simulations which agreed very closely with the an...

Scattering of sine-Gordon breathers on a potential well.

We analyze the scattering of the classical sine-Gordon breathers on a square potential well. We show that the scattering process depends not only on the vibration frequency of the breather and its incoming speed but also on its phase as well as the depth and width of the well. We show that the breather can pass through the well and exit with a speed different, sometimes larger, from the initial...

Oscillating and rotating sine-Gordon system.

Inverse scattering and the symplectic form for sine-Gordon solitons

We consider the canonical symplectic form for sine-Gordon evaluated explicitly on the solitons of the model. The integral over space in the form, which arises because the canonical argument uses the Lagrangian density, is done explicitly in terms of functions arising in the group doublecrossproduct formulation of the inverse scattering procedure, and we are left with a simple expression given b...

Existence of internal modes of sine-gordon kinks

We study whether or not sine-Gordon kinks exhibit internal modes or "quasimodes." By considering the response of the kinks to ac forces and initial distortions, we show that neither intrinsic internal modes nor "quasimodes" exist in contrast to previous reports. However, we do identify a different kind of internal mode bifurcating from the bottom edge of the phonon band which arises from the di...