# Inverse scattering solution of the weak noise theory of the Kardar-Parisi-Zhang equation with flat and Brownian initial conditions

@inproceedings{Krajenbrink2021InverseSS, title={Inverse scattering solution of the weak noise theory of the Kardar-Parisi-Zhang equation with flat and Brownian initial conditions}, author={Alexandre Krajenbrink and Pierre Le Doussal}, year={2021} }

We present the solution of the weak noise theory (WNT) for the Kardar-Parisi-Zhang equation in one dimension at short time for flat initial condition (IC). The non-linear hydrodynamic equations of the WNT are solved analytically through a connexion to the Zakharov-Shabat (ZS) system using its classical integrability. This approach is based on a recently developed Fredholm determinant framework previously applied to the droplet IC. The flat IC provides the case for a non-vanishing boundary… Expand

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