The solutions for nonlinear Schrödinger equations

We consider the nonlinear Schrödinger equation equation(*){iut+Δu±f(u)=0,f(u)=∣u∣2mun,m,n∈N,(x,t)∈RN×Ru(0,x)=u0(x). We give a formal solution of the Cauchy problem (*). By this formal solution, we obtain that there exists a constant BB independent of p,Np,N such that for any initial data ‖u0‖Hs