Solitons and topology: Observation of cnoidal wave localization in non-linear topolectric circuits

Topological phases have been realized in a variety of classical metamaterials. They provide easily accessible platforms to study topology in regimes beyond experimental limitations of real materials. While most implementations are limited to the linear regime, investigating non-linear effects promises to reveal a plethora of new phenomena, such as solitons and chaos. To study the intertwining of topology and non-linearity we engineered a topolectric circuit reminiscent of the Su-Schrieffer-Heeger (SSH) model with added tunable onsite non-linearity. We observe the localized cnoidal (LCn) state which maintains the spatial exponential localization of the SSH edge mode while distorting a sinusoidal input into eccentric waves in time domain. In this talk, we complement the non-linear differential equations with the theory of topological localization and develop an analytic description of the LCn state.