Accurate and efficient evolution of nonlinear Schrodinger equations

An evolution method is presented for affecting nonlinear Schrodinger evolution on an initial wave function applicable to a wide range of problems. At Chebyshev quadrature points of a given time interval, the method samples wave function that achieves optimal degree of representation. An implicit equation representing an integral Schrodinger equation is given for sampled wave function at the sampling points. Several examples and demonstrations of the method and its numerical evaluation on Gross-Pitaevskii equation for a Bose-Einstein condensate are demonstrated.