  We explore the weak-strong-coupling Bose-Fermi duality in a model of a
single-channel integer or fractional quantum Hall edge state with a
finite-range interaction. The system is described by a chiral Luttinger liquid
with non-linear dispersion of bosonic and fermonic excitations. We use the
bosonization, a unitary transformation, and a refermionization to map the
system onto that of weakly interacting fermions at low temperature $T$ or
weakly interacting bosons at high $T$. We calculate the equilibration rate
which is found to scale with temperature as $T^5$ and $T^{14}$ in the
high-temperature ("bosonic") and the low-temperature ("fermonic") regimes,
respectively. The relaxation rate of a hot particle with the momentum $k$ in
the fermonic regime scales as $k^7T^7$.
