Simulation of the quench dynamics and a plot of the amplitude remaining at the edge sites in the long-term limit after a quench in the u – w plane. The light-blue lines indicate the parameters where we can obtain the exact edge-localized solutions. The white numbers show the nonlinear Chern number, and the grey lines represent their phase boundaries, where we relate the amplitude w to w edge = j ( x = 0) 2 at t = 0. These lines agree with the boundary of the topological phase, and thus, the quench dynamics shows the shift in the phase boundary by nonlinearity. We take the different initial configurations corresponding to the edge modes in the linear limit at u = -1 in d and u = 1 in e. Thus, the phase diagrams of the quench dynamics reproduce the topological phases with different Chern numbers in these panels ( C = -1 for d and C = 1 for e ).
