Solitons with Self-induced Topological Nonreciprocity

The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation. This nonreciprocal behavior, dependent on soliton power, arises from the interplay between linear and nonlinear terms in the equations of motion. Initially stable at high power, solitons exhibit nonreciprocal instabilities as power decreases, leading to unidirectional acceleration and amplification. This behavior is topologically protected by winding numbers on the solitons' mean-field Hamiltonian and their stability matrix, linking nonlinear dynamics and point gap topology in non-Hermitian Hamiltonians.