# Quantized soliton pumping governed by high-dimensional Chern invariants

## TL;DR

This paper demonstrates quantized soliton transport governed by high-dimensional topological invariants in nonlinear systems, observed through engineered circuits.

## Contribution

The work introduces a novel framework for soliton pumping governed by first and second Chern numbers in orthogonal dimensions.

## Key findings

- Phase transitions in soliton pumping include integer, fractional, and trapping states.
- Anisotropic soliton pumping with integer and fractional transport along orthogonal axes is demonstrated.
- Nonlinear topolectrical circuits enable direct observation of quantized soliton transport.

## Abstract

Non-linear topological pumping—a quantized transport phenomenon of solitary waves in parametrically driven systems—represents a critical interface bridging topological physics and non-linear dynamics. While the first Chern number-governed soliton transport has been extensively studied, the fundamental interplay between high-dimensional band topology and soliton pumping remains unexplored. Here, we establish a theoretical framework and experimental demonstration of soliton topological pumping simultaneously governed by first and second Chern numbers in orthogonal dimensions. Through the modulation of non-linear strength, the system exhibits phase transitions spanning integer-quantized soliton pumping, fractional-quantized soliton pumping and soliton trapping states. Furthermore, by engineering linear band structures, we demonstrate anisotropic soliton pumping where quantized transport manifests integer and fractional characteristics along orthogonal spatial axes. Experimentally, we implement non-linear time-modulated topolectrical circuits whose dynamical equations maintain precise isomorphism with theoretical lattice models, enabling the direct observation of integer, fractional and integer/fractional soliton pumping. Our work establishes a scalable experimental platform for investigating advanced non-linear topological phases, which may be broadly applied to systems at the interface between topological matter and non-linear wave physics.

We reveal quantized soliton pumping governed by high-dimensional Chern invariants, and experimentally observe integer, fractional, and anisotropic soliton pumping in time-modulated nonlinear topolectrical circuits.