In this Letter, we demonstrate that the synergetic interplay of topology, nonreciprocity, and nonlinearity is capable of unprecedented effects. We focus on a nonreciprocal variant of the Su-Shrieffer-Heeger chain with local Kerr nonlinearity. We find a continuous family of nonreciprocal edge solitons (NESs) emerging from the topological edge mode, with near-zero energy, in great contrast from their reciprocal counterparts. Analytical results show that this energy decays exponentially towards zero when increasing the lattice size. Consequently, despite the absence of chiral and sublattice symmetries within the system, we obtain zero-energy NESs, which are insensitive to growing Kerr nonlinearity. Even more surprising, these zero-energy NESs also persist in the strong nonlinear limit. Our work may enable different avenues for the control of nonlinear topological waves without requiring the addition of complex chiral- or sublattice-preserving nonlinearities.

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• Edge states
• Kerr effect
• Skin effect
• Topological insulators
• Topological phases of matter
• Non-Hermitian systems
• Solitons
• Waveguides