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We study properties of the localized solitons to the sine-Gordon equationexcited on the attractive impurity by a moving kink. The cases of one- andtwo-dimensional spatially extended impurities are considered. For the case ofone-dimensional impurity the possibility of excitation of the first even andodd high-amplitude impurity modes by the moving kink is demonstrated. For thecase of two-dimensional impurity we show the possibility of excitation of thenonlinear high-amplitude waves of new type called here breathing pulson andbreathing 2D soliton. We suggest different analytical expressions to modelthese nonlinear excitations. The dependencies of the oscillation frequency andthe amplitude of the excited impurity modes on the impurity parameters arereported.

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