Solutions of the 1D Coupled Nonlinear Schrödinger Equations by the CIP-BS Method (Communications in Computational Physics, 2018)
In this paper, we present solutions for the one-dimensional coupled nonlinearSchrödinger (CNLS) equations by the Constrained Interpolation Profile-Basis Set(CIP-BS) method. This method uses a simple polynomial basis set, by which physicalquantities are approximated with their values and derivatives associated with gridpoints. Nonlinear operations on functions are carried out in the framework of differentialalgebra. Then, by introducing scalar products and requiring the residue to beorthogonal to the basis, the linear and nonlinear partial differential equations are reducedto ordinary differential equations for values and spatial derivatives. The methodgives stable, less diffusive, and accurate results for the CNLS equations.