  We investigate the topological physics and the nonlinearity-induced trap
phenomenon in a coupled system of pendulums. It is described by the dimerized
sine-Gordon model, which is a combination of the sine-Gordon model and the
Su-Schrieffer-Heeger model. The initial swing angle of the left-end pendulum
may be regarded as the nonlinearity parameter. The topological number is well
defined as far as the pendulum is approximated by a harmonic oscillator. The
emergence of the topological edge state is clearly observable in the
topological phase by solving the quench dynamics starting from the left-end
pendulum. A phase diagram is constructed in the space of the swing angle $\xi
\pi $ with $|\xi |\leq 1$ and the dimerization parameter $\lambda $ with
$|\lambda |\leq 1$. It is found that the topological phase boundary is rather
insensitive to the swing angle for $% |\xi |\lesssim 1/2$. On the other hand,
the nonlinearity effect becomes dominant for $|\xi |\gtrsim 1/2$, and
eventually the system turns into the nonlinearity-induced trap phase.
Furthermore, when the system is almost dimerized ($\lambda \simeq 1$), coupled
standing waves appear and are trapped to a few pendulums at the left-end,
forming the dimer phase. Its dynamical origin is the cooperation of the
dimerization and the nonlinear term.

Mesoscale and Nanoscale Physics