The Rayleigh-Ritz variational procedure is applied to solve the Zakharov-Shabat scattering problem. An approximate solution is assumed as a linear combination of basis functions, leading to a homogeneous system of linear equations for eigenfunctions and an algebraic equation for eigenvalues. The effectiveness of the variational approach is illustrated by calculating the discrete spectrum of the Zakharov-Shabat system. Several numerical examples for various pulse-shaped potentials are given to demonstrate the practical usefulness of the method.
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Marek Adam. Jaworski (1997) studied this question.