Solitons with Self-induced Topological Nonreciprocity

The nonlinear Schrodinger equation can support solitons, self-interacting states that remain sharply localized and behave as nearly independent objects. Here, we demonstrate the existence of solitons with self-induced nonreciprocal dynamics in a discrete version of the nonlinear Schrodinger equation. This nonreciprocal behavior depends on the soliton's power, indicating an interplay between linear and nonlinear terms in the Hamiltonian. Starting from static stable solitons at high power, the nonreciprocal behavior manifests as the power is lowered first by the appearance of nonreciprocal linear instabilities on static solitons and then by a full self-induced nonreciprocal regime, in which the solitons propagate with unidirectional acceleration and amplification. We show this behavior to be topologically protected by winding numbers on the solitons' mean-field Hamiltonian and their linear stability matrix, revealing an intimate connection between nonlinear, nonreciprocal dynamics and point gap topology in non-Hermitian linear Hamiltonians.