Well-posedness of the Cauchy problem of high dimension non-isotropic fourth-order Schrödinger equations in Sobolev spaces

We study the well-posedness for the Cauchy problem of the non-isotropically perturbed nonlinear Schrödinger equation iut+Δu+|u|αu+a∑i=1duxixixixi=0, where a is a real constant, 1≤d