  It has been discovered that the Kadomtsev-Petviashvili(KP) equation governs
the distribution of the fluctuation of many random growth models, in
particular, the Tracy-Widom distributions appear as special self-similar
solutions of the KP equation. We prove that the anti-derivative of Baik-Rains
distribution, which governs the fluctuation of the models in the KPZ
universality class starting with stationary initial data, satisfies the KP
equation. We start from a determinantal formula of the generating function of
the KPZ equation, which satisfies the KP. Then we observe that the equation
still holds in the large time limit.
