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Topological transport of solitons in composite linear-nonlinear lattices

Yaroslav V. Kartashov1, Vladimir V. Konotop2,*, and Dmitry A. Zezyulin3,†

  • 1Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia
  • 2Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, 1749-016 Lisboa, Portugal
  • 3School of Physics and Engineering, ITMO University, St. Petersburg 197101, Russia

  • *Contact author: vvkonotop@ciencias.ulisboa.pt
  • †Contact author: dzezyulin@itmo.ru
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Phys. Rev. A 114, L021302 – Published 13 August, 2026

DOI: https://doi.org/10.1103/msxp-m5h1

Abstract

Quantized transport usually occurs in linear periodic systems with nontrivial topology. While nonlinearity can strongly influence this transport, particularly through the formation of solitons, it is still determined by the spatiotemporal Chern indices of the bands of the underlying linear potential. Here, we show that nonlinear quantized transport can be induced by a sliding nonlinear lattice, even when the latter is combined with a static linear lattice, whose bands are topologically trivial. In such a system, an effective topology emerges from characteristic features of stable Wannier solitons and can be described in terms of the transport of Wannier centers associated with a composite potential combining the stationary linear lattice and an effective moving nonlinear lattice. The phenomenon is generic, as confirmed by the analysis of the continuous Gross-Pitaevskii equation with mutually sliding nonlinear and linear lattices, as well as by the corresponding discrete model with spatially varying coefficients. By increasing the norm of the input state, i.e., the nonlinearity strength, one can observe the unique transition from the absence of transport, to the topological transport, and, eventually, to the nontopological dragging of the input state by the nonlinear lattice.

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Phys. Rev. A 114, L021302– Published 13 August, 2026
  • Received 13 April 2026
  • Accepted 29 July 2026
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