Hi, I am reading a book about optics. I tried to solve the following differential equation using Mathematica. For some reason, it didn't work. It seems that the solver can't handle the absolute value of a complex variable in a differential equation. it would helpful, if I get a possible solution. Thanks.
NDSolve[I D[u[\[Xi], \[Tau]], \[Xi]] + 1/2 D[u[\[Xi], \[Tau]], {\[Tau], 2}] +
Abs[u[\[Xi], \[Tau]]]^2 u[\[Xi], \[Tau]] == 0, u, {\[Xi], 0, 10}, {\[Tau], 0, 10}]
