Evolution of a Sine-Gordon Breather under the Action of Conservative Perturbations

Abstract

Dynamics of a sine-Gordon breather under the action of different conservative perturbations is studied. General description of the perturbation-induced breather's evolution (radiative decay) starting from an initial state in the form of a low-frequency breather and finishing at the final asymptotic stage of decay of the small-amplitude one is presented.

Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

“…10 In connection with studying real physical quasi-1D systems such as long Josephson junctions and quasi-1D ferromagnets there emerged many works treating behavior of sG breathers under action of perturbations breaking exact integrability: dissipative and diverse conservative terms ͑see Ref. [11][12][13], and references therein͒. Analytical treatment of the problem is possible if one considers the corresponding perturbation in the inverse scattering transform 11 or if one obtains the multiple-scale asymptotic expansion 12 in the limit of high breather frequencies.…”

“…It is also possible to derive some estimates in general case. 13 As one can easily predict, the breather lifetime proved to be long if perturbation is small. In nonintegrable models with background potentials sufficiently different from the sine function breatherlike long-living nonlinear excitations are observed numerically ͑the 4 model-Ref.…”

Breather Induced Modification of the Speed of Sound

“…As we can see, the presence of the breather increases the speed of sound where the degree of the modifications strongly depends on the internal breather frequencies ͑k br p 1 2 v 2 br ͒. The largest values are achieved in the high and low frequency limit, where the breather is stable [1,10,11]. Outside of this limit the radiation-induced losses of the breather energy cannot be neglected and the breather slow decays.…”

“…In this case we can distinguish two different kinds of breathers, those with small amplitudes and those with large amplitudes. For the small amplitude (the high frequency) breather where the breather size is much larger than the lattice space, the effects of discreteness are almost negligible and we can use the well known solution from the SG model [1,10]. For the large amplitude (the low frequency limit), the breather can be treated as a pair of kink and antikink trapped in the wells of the potentials [1,11].…”