We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

We show that the one dimensional unitary matrix model with potential of the form aU + bU2 + h.c. is integrable. By reduction to the dynamics of the eigenvalues, we establish the integrability of a system of particles in one space dimension in an external potential of the form a cos(x+α) + b cos(2x+ β) and interacting through two-body potentials of the inverse sine square type. This system const...