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Instanton filtering for the stochastic Burgers equation
We address the question whether one can identify instantons in direct
numerical simulations of the stochastically driven Burgers equation. For this
purpose, we first solve the instanton equations using the Chernykh-Stepanov
method [Phys. Rev. E 64, 026306 (2001)]. These results are then compared to
direct numerical simulations by introducing a filtering technique to extract
prescribed rare events from massive data sets of realizations. Using this
approach we can extract the entire time history of the instanton evolution
which allows us to identify the different phases predicted by the direct method
of Chernykh and Stepanov with remarkable agreement
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