Charge-varying sine-Gordon deformed defects

Sine-Gordon deformed defects that exhibit unusual phenomenological features on the topological charge are investigated. The possibility of a smooth and continuous transition between topological (non-null charge) and non-topological (null charge) scenarios of deformed defects supported by sine-Gordon structures is evinced by the analytical calculation of topological charges and localized energy distributions. By describing cyclic deformation chains, we show that a triggering sine-Gordon model simultaneously supports kink- and lump-like defects, whose topological mass values are closed by trigonometric or hyperbolic successive deformations. In spite of preserving analytical closure relations constraining the topological masses of 3- and 4-cyclically deformed defects, the deformation chains produce kinks and lumps which exhibit non-monotonic behavior and extra inflection points. The outcome of our analysis suggests that cyclic deformations create novel scenarios of physical and mathematical applicability of defect structures supported by the sine-Gordon theory.