ArticleNature communications2022
Topological invariant and anomalous edge modes of strongly nonlinear systems.
Article in Nature communications, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Protected Chaos in a Topological Lattice.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- Transition from the topological to the chaotic in the nonlinear Su-Schrieffer-Heeger model.Nature communications · 2025Article
- Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
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4 authors.
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Abstract
Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk waves and characterize topological phases in one-dimensional (1D) generalized nonlinear Schrödinger equations in the strongly nonlinear regime, where the general nonlinearities are beyond Kerr-like interactions. Without utilizing linear analysis, we develop an analytic strategy to demonstrate the quantization of nonlinear Berry phase due to reflection symmetry. Mode amplitude itself plays a key role in nonlinear modes and controls topological phase transitions. We then show bulk-boundary correspondence by identifying the associated nonlinear topological edge modes. Interestingly, anomalous topological modes decay away from lattice boundaries to plateaus governed by fixed points of nonlinearities. Our work opens the door to the rich physics between topological phases of matter and nonlinear dynamics.
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