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Modulational Instability and Growth Blockade in the Nonlinear Hatano-Nelson Model

What happens when a Kerr nonlinearity is added to the Hatano-Nelson lattice with asymmetric hopping under periodic boundary conditions. A linear stability analysis shows the nonlinear plane waves are modulationally unstable, and the resulting self-induced disorder produces a growth blockade: the norm growth driven by the non-Hermitian gain halts abruptly, a stopping of convective motion with no counterpart in the linear model.