Hoping that it can be helpful, I attach a code for parallel integration of the non-linear Schrodinger equation in a circular domain using PETSc/SLEPc.
fiber-circle-time-SLEPc.edp (9.0 KB)
The code uses an implicit midpoint integrator and initializes the wavefunction to an eigenvector of the linear Schrodinger equation (or their linear combination).
Best wishes,
Alexei