A conservative exponential time differencing method for the nonlinear cubic Schrodinger equation

A mass and energy conservative exponential time differencing scheme using the method of lines is proposed for the numerical solution of a certain family of first-order time-dependent PDEs. The resulting nonlinear system is solved with an unconditionally stable modified predictor-corrector method using a second-order explicit scheme. The efficiency of the method introduced is analyzed and discussed by applying it to the nonlinear cubic Schrodinger equation. The results arising from the experiments for the single, the double soliton waves and the system of two Schrodinger equations are compared with relevant known ones.