  We consider non-linear ballistic spin transport in the XXZ spin chain and
derive an analytical result for the non-linear Drude weight $D^{(3)}$ at
infinite temperatures. In contrast to the linear Drude weight $D^{(1)}$, we
find that the result not only depends on anisotropy but also on the string
length of the quasiparticles transporting the spin current. Our result provides
further insights into transport by quasiparticles and raises questions about
Luttinger liquid universality.

Strongly Correlated Electrons;Statistical Mechanics