The nonlinear Schrödinger equation supports solitons—self-interacting, localized states that behave as nearly independent objects. Here, we show the existence of solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrödinger equation. This nonreciprocal behavior, dependent on soliton power and symmetry, occurs when parity is broken in a lattice with an Ablowitz-Ladik type of nonlinearity. 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.

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• Non-reciprocal propagation
• Optical & microwave phenomena
• Skin effect
• Topological phases of matter
• 1-dimensional systems
• Non-Hermitian systems
• Nonlinear waves
• Solitons
• Mean field theory