Abstract Nonlinear topological pumping—a quantized transport phenomenon of solitary waves in parametrically-driven systems—represents a critical interface bridging topological physics and nonlinear 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 nonlinear 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 nonlinear 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 nonlinear topological phases, which may be broadly applied to systems at the interface between topological matter and nonlinear wave physics.
Di et al. (Mon,) studied this question.