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We propose a new high-precision algorithm for solving the initial problem forthe Zakharov-Shabat system. This method has the fourth order of accuracy and isa generalization of the second order Boffetta-Osborne scheme. It is allowed byour method to solve more effectively the Zakharov-Shabat spectral problem forcontinuous and discrete spectra.

Novel Numerical Algorithm with Fourth-Order Accuracy for the Direct Zakharov-Shabat Problem