  Nonlinearities in lattices with topologically nontrivial band structures can
give rise to topological solitons, whose properties differ from both
conventional lattice solitons and linear topological boundary states. We show
that a Su-Schrieffer-Heeger-type lattice with both nonlinearity and
nonreciprocal non-Hermiticity hosts a novel oscillatory soliton, which we call
a topological end breather. The end breather is strongly localized to a
self-induced topological domain near the end of the lattice, in sharp contrast
to the extended topological solitons previously found in one-dimensional
lattices. Its stable oscillatory dynamics can be interpreted as a Rabi
oscillation between two self-induced topological boundary states, emerging from
a combination of chiral lattice symmetry and the non-Hermitian skin effect.
This demonstrates that non-Hermitian effects can give rise to a wider variety
of topological solitons than was previously known to exist.
