Abstract Bistability is a key property of many systems arising in the nonlinear sciences. For example, it appears partial differential equations (PDEs). scalar bistable reaction-diffusions PDEs, case even has taken on different names within communities such as Allee, Allen-Cahn, Chafee-Infante, Nagumo, Ginzburg-Landau, $$\Phi ^4$$ <mml:m...