  We study the effect on the chiral edge states by including a nonlinearity to
a Chern insulator which has two chiral edge states with opposite chiralities.
We explore a quench dynamics by giving a pulse to one site on an edge and
analyzing the time evolution of a wave packet. Without the nonlinearity, an
initial pulse spreads symmetrically and diffuses. On the other hand, with the
nonlinearity present, a solitary wave is formed by the self-trapping effect of
the nonlinear term and undergoes a unidirectional propagation along the edge,
which we identify as a chiral edge soliton. A further increase of the
nonlinearity induces a self-trapping transition, where the chiral wave packet
stops its motion. It is intriguing that the nonlinearity is controlled only by
changing the initial condition without changing a sample.
