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We study the topological physics in nonlinear Schr\"{o}dinger systems onlattices. We employ the quench dynamics to explore the phase diagram, where apulse is given to a lattice point and we analyze its time evolution. There aretwo system parameters $\lambda $ and $\xi $, where $\lambda $ controls thehoppings between the neighboring links and $\xi $ controls the nonlinearity.The dynamics crucially depends on these system parameters. Based on analyticaland numerical studies, we derive the phase diagram of the nonlinearSu-Schrieffer-Heeger (SSH) model in the ($\lambda ,\xi $) plane. It consists offour phases. The topological and trivial phases emerge when the nonlinearity$\xi $ is small. The nonlinearity-induced localization phase emerges when $\xi$ is large. We also find a dimer phase as a result of a cooperation between thehopping and nonlinear terms. A similar analysis is made of the nonlinearsecond-order topological system on the breathing Kagome lattice, where a trimerphase appears instead of the dimer phase.

Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system