On a nonlocal, nonlinear Schroedinger equation occurring in plasma physics

We study some generalizations of the equation: iφt+δφ=-div(I2∇ψI2∇ψ)δψ=φ and we show that the local in time Cauchy problem is well posed in the suitable spaces. We give some regularity and scattering results. We prove the existence of standing waves and we study their stability. We show that for some initial values, the solution blows up in finite time