Higher-order hyperbolic topological solitonic insulators

Recent investigations have shown that higher-order topological solitonic insulators can be created in nonlinear media. However, current discussions on higher-order topological solitons only focus on Euclidean spaces. In this work, we theoretically propose and numerically demonstrate the construction of higher-order topological solitons in engineered hyperbolic lattices, which are regular tessellations in non-Euclidean space with a constant negative curvature. In particular, two types of hyperbolic lattices, {4, 5} and {8, 3}, are applied to design higher-order topological solitonic insulators. We demonstrate that for both types of lattices, higher-order topological solitons can bifurcate from linear corner states under either self-focusing or self-defocusing nonlinear conditions, with their localization being controllable by the initial input power. We also observe that the rotational symmetry of these topological solitons remains unaffected by variations in the initial input power. Our work theoretically extends higher-order topological soliton insulators to non-Euclidean space, breaking through the limitation in traditional Euclidean space where only topological solitons with threefold, fourfold, and sixfold rotational symmetries can be realized. This enables the realization of topological solitons with higherfold rotational symmetries. It provides a theoretical foundation for the design of experimentally feasible platforms for higher-order hyperbolic topological solitonic insulators, and is anticipated to have potential applications in designing highly efficient soliton devices with strong robustness.