B-SPLINE FINITE-ELEMENT STUDIES OF THE NONLINEAR SCHRODINGER-EQUATION

The non-linear Schrodinger equation is solved numerically by a B-splin e finite element method. The approach used is based on collocation of cubic B-splines over spatial finite elements so that we have continuit y of the dependent variable and its first two derivatives throughout t he solution range. Time integration of the resulting system of ordinar y differential equations is effected using a Crank-Nicolson approximat ion. Standard problems are used to validate the algorithm. Comparisons are made with published numerical and analytical solutions. The propo sed method exhibits good conservation properties and performs well. Th e development of temporally recurrent states from spatially periodic i nitial conditions is examined through computer experiments. The birth of mobile as well as static solitons out of Maxwellian initial data is observed.