Dimensional Synthesis for Emulating Nonlinear Disclination Dynamics

Nonlinearity plays a central role in topological defect states, governing their stability, localization, and dynamics beyond the linear regime. However, investigating nonlinear dynamics of states in three- and higher-dimensional systems remains highly challenging due to fabrication difficulties and the constraints imposed by spatial dimensionality. Here, we overcome this limitation by employing one-dimensional synthesized lattices (1DSLs). Using anchor-site and anchor-mode mappings, we demonstrate that 1DSLs provide a versatile one-dimensional platform for emulating the essential nonlinear dynamics and mode-coupling pathways of disclination states in higher-dimensional topological lattices. We show that different disclination states exhibit distinct nonlinear dynamics and mode-coupling pathways, all of which are faithfully reproduced in the mapped 1DSLs. In particular, corner and disclination states exhibit fundamentally different nonlinear coupling mechanisms, whereas three-dimensional disclination lattices support additional interactions between different classes of defect states. Our work extends dimensional synthesis beyond linear emulation and establishes a practical one-dimensional platform for investigating nonlinear topological defect physics in higher dimensions. More broadly, it provides a route for exploring nonlinear topological phenomena that are otherwise difficult to access in higher-dimensional photonic, acoustic, and mechanical wave systems.