A new method to solve the direct Zakharov–Shabat scattering problem is proposed based on the solution for coupled Gel’fand–Levitan–Marchenko integral equations. Speedup of computations is achieved by using the Töplitz symmetry of the matrix and an “inner bordering” procedure. The new algorithm was tested on the exactly solvable potential. It is shown that the suggested algorithm significantly surpasses the traditional transfer matrix method in efficiency.
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Фрумин et al. (2015) studied this question.
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