  Nonlinear topology has been much less inquired compared to its linear
counterpart. Existing advances have focused on nonlinearities of limited
magnitudes and fairly homogeneous types. As such, the realizations have rarely
been concerned with the requirements for nonlinearity. Here we explore
nonlinear topological protection through the determination of nonlinear rules
and demonstrate their relevance in real-world experiments. We take advantage of
chiral symmetry and identify the condition for its continuation in general
nonlinear environments. Applying it to one-dimensional topological lattices, we
can obtain definite evolution paths of zero-energy edge states that preserve
topologically nontrivial phases regardless of the specifics of the chiral
nonlinearities. Based on an acoustic prototype design, we theoretically,
numerically, and experimentally showcase the nonlinear topological edge states
that persist in all nonlinear degrees and directions without any frequency
shift. Our findings unveil a broad family of nonlinearities that are compatible
with topological non-triviality, establishing a solid ground for future
drilling in the emergent field of nonlinear topology.
