  In this work, 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 non-reciprocal 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 symmetry 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 new avenues for the control of nonlinear
topological waves without requiring the addition of complex chiral-preserving
nonlinearities.
