A Wavelet-Galerkin Method for the Nonlinear Schrödinger Equation

A general implementation is presented for constructing a wavelet method for solving the nonlinear equation of Schr¨odinger. An explicit formula is derived which yields a stability in of the numerical solution. A simulation is elaborated to show the general behavior of the distribution function. Numerical results and comparison with classical algorithms are provided. This approach prove an attractive scheme for solving such equation.