Exponential Fourth Order Schemes for Direct Zakharov-Shabat problem

08/30/2019

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by   Sergey Medvedev, et al.

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We propose two finite-difference algorithms of fourth order of accuracy for solving the initial problem of the Zakharov-Shabat system. Both schemes have the exponential form and conserve quadratic invariant of Zakharov-Shabat system. The second scheme contains the spectral parameter in exponent only and allows to apply the fast computational algorithm.