  We study the effect of the magnon-magnon interaction on the nonlinear magnon
transport. The magnon-magnon interaction induces nonreciprocal magnon decay
when the time-reversal symmetry is broken, and leads to nonlinear thermal
responses of magnons. We construct a theoretical framework to study the
nonlinear thermal responses due to the nonreciprocal magnon decay by using the
imaginary Dyson equation and quantum kinetic theory, which is then applied to a
model of honeycomb ferromagnets with Dzyaloshinskii-Moriya interactions. An
order estimate shows that the nonlinear thermal response from the present
mechanism is feasible for experimental measurement.
