On the computation of the solution of perturbed nonlinear Schrödinger equations

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Abstract We introduce a numerical treatment for solving nonlinear Schrödinger equations in the form $i\, \psi_{t} + a_{0}\psi_{xx} - v (x) \psi - a_{1} |\psi|^{2}\psi = f (x, \, t),$ where f(x,t) is an arbitrary function, being perturbative, dependent on ψ. For this purpose, we developed a MAPLE® procedure and examined the effectiveness of the method on two problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010