Accurate and efficient evolution of nonlinear Schrodinger equations

A numerical method is given for affecting nonlinear Schrodinger evolution on an initial wave function, applicable to a wide range of problems, such as time-dependent Hartree, Hartree-Fock, density-functional, and Gross-Pitaevskii theories. The method samples the evolving wave function at Chebyshev quadrature points of a given Lime interval. This achieves an optimal degree of representation. At these sampling points, an implicit equation, representing an integral Schrodinger equation, is given for the sampled wave function. Principles and application details are described, and several examples and demonstrations of the method and its numerical evaluation on the Gross-Pitaevskii equation for a Bose-Einstein condensate are shown.