This paper shows that the Kadomtsev -Petvlashvili equation of type I governs the evolution of certain weakly nonlinear fluctuations on a staticor very slowly varying cosmological background. The model consists of a mixture of nonrelativistic, collisionless (here after called “dark”) matter at nonzero temperature together with a smaller amount of zero-temperature rotation- free dust. The two components are coupled only by gravitational forces.