Excitation of high-amplitude localized nonlinear waves as a result of interaction of kink with attractive impurity in sine-Gordon equation

We study properties of the localized solitons to the sine-Gordon equation excited on the attractive impurity by a moving kink. The cases of one- and two-dimensional spatially extended impurities are considered. For the case of one-dimensional impurity the possibility of excitation of the first even and odd high-amplitude impurity modes by the moving kink is demonstrated. For the case of two-dimensional impurity we show the possibility of excitation of the nonlinear high-amplitude waves of new type called here breathing pulson and breathing 2D soliton. We suggest different analytical expressions to model these nonlinear excitations. The dependencies of the oscillation frequency and the amplitude of the excited impurity modes on the impurity parameters are reported.