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Fundamental modifications of the standard Schr\"odinger equation byadditional nonlinear terms have been considered for various purposes over therecent decades. It came as a surprise when, inverting Abner Shimony'sobservation of "peaceful coexistence" between standard quantum mechanics andrelativity, N. Gisin proved in 1990 that any (deterministic) nonlinearSchr\"odinger equation would allow for superluminal communication. This is bynow the most spectacular and best known anomaly. We discuss further anomalies,simple but foundational, less spectacular but not less dramatic.

Nonlinear Schr\"odinger equation in foundations: summary of 4 catches