Energy minimization related to the nonlinear Schrِdinger equation

In this the window of the Sobolev gradient technique to the problem of minimizing a Schrِdinger functional associated with a nonlinear Schrِdinger equation. We show that gradients act in a suitably chosen Sobolev space (Sobolev gradients) can be used in finite-difference and finite-element settings in a computationally efficient way to find minimum energy states of Schrِdinger functionals.