Wobbles and other kink-breather solutions of the sine-Gordon model

Abstract

We study various solutions of the sine-Gordon model in ͑1+1͒ dimensions. We use the Hirota method to construct some of them and then show that the wobble, discussed in detail in a recent paper by Kälberman, is one of such solutions. We concentrate our attention on a kink and its bound states with one or two breathers. We study their stability and some aspects of their scattering properties on potential wells and on fixed boundary conditions.

Shape and wobbling wave excitations in Josephson junctions: Exact solutions of the(2+1)-dimensional sine-Gordon model

“…3,4 Such solutions have been discussed earlier in the literature in the context of wobbling modes of a sine-Gordon soliton. [25][26][27] The ͑1+1͒D soliton wobbling mode can be written in the following symmetric form ͑x,t͒ = 4 arctan where is given by…”

Untitled

“…A solution that is a bound state of a breather and kink, the sine-Gordon wobble, is described in [23]. These solutions show interesting behaviour when they are interacting with square wells [16,17].…”

“…The authors found that back-reflection for some incoming velocities also arises for this system and gave two effective models to account for this phenomenon. Soliton interactions with rectangular wells have also been discussed for various other soliton systems [12,13,14,15,16,17,18]. A kink interacting with a smooth well is discussed in [19] in terms of the sineGordon model and in [20] for the λφ 4 model.…”

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

“…4 Because of the integrability, wobbling kinks in the sine-Gordon equation do not radiate continuous waves. [7][8][9]15 Radiation does not exist in the integrable system due to the absence of internal modes. 6,10 Radiation damping due to resonances in discrete Klein-Gordon equations was discussed in Ref.…”