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

Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Mar;77(3 Pt 2):036613. doi: 10.1103/PhysRevE.77.036613. Epub 2008 Mar 27.

Abstract

We study various solutions of the sine-Gordon model in (1+1) 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.