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We consider a model for a two-dimensional Kagome-lattice with defocusingnonlinearity, and show that families of localized discrete solitons maybifurcate from localized linear modes of the flat band with zero powerthreshold. Each family of such fundamental nonlinear modes corresponds to aunique configuration in the strong-nonlinearity limit. By choosing well-tuneddynamical perturbations, small-amplitude, strongly localized solutions fromdifferent families may be switched into each other, as well as moved betweendifferent lattice positions. In a window of small power, the lowest-energystate is a symmetry-broken localized state, which may appear spontaneously.

Discrete flat-band solitons in the Kagome lattice