  Topological states have been widely investigated in different types of
systems and lattices. In the present work, we report on topological edge states
in double-wave (DW) chains, which can be described by a generalized
Aubry-Andr\'e-Harper (AAH) model. For the specific system of a
driven-dissipative exciton polariton system we show that in such potential
chains, different types of edge states can form. For resonant optical
excitation, we further find that the optical nonlinearity leads to a
multistability of different edge states. This includes topologically protected
edge states evolved directly from individual linear eigenstates as well as
additional edge states that originate from nonlinearity-induced localization of
bulk states. Extending the system into two dimensions (2D) by stacking
horizontal DW chains in the vertical direction, we also create 2D multi-wave
lattices. In such 2D lattices multiple Su-Schrieffer-Heeger (SSH) chains appear
along the vertical direction. The combination of DW chains in the horizontal
and SSH chains in the vertical direction then results in the formation of
higher-order topological insulator corner states. Multistable corner states
emerge in the nonlinear regime.
