Impurity effects on soliton dynamics in planar ferromagnets
Abstract We investigate numerically the dynamics of solitons in a ferromagnetic spin chain and we show that the sine-Gordon approximation provides only a poor description of the solitary excitations in the presence of impurities. Depending on their energy and the strength of the impurity, solitons can be reflected or transmitted. When they are reflected, they can suffer abrupt changes in velocity, which are associated to the switch from one soliton branch to another. In some cases the scattering by an impurity can excite an internal mode of the soliton, which is able to store some energy and modify the output of the scattering.
Discreteness effects on a sine-Gordon breather
We employ collective-variable theory to describe the dynamics of a breather excitation in its center-of-mass frame in continuous and discrete systems of one spatial dimension. The exact equations of motion for the collective variable and coupled phonon field are derived for any system which supports breatherlike excitations that have even spatial parity where the collective variable represents half the distance between the breather subkinks. We then specialize the theory to the sine-Gordon (SG) case. For the continuum SG system we derive the exact effective potential in terms of the collective variable and discuss the relativistic effects on the breather subkinks which are quite different t…