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arXiv · 1909.13228

Fast Computation of the Direct Scattering Transform by Fourth Order Conservative Multi-Exponential Scheme

Sergey Medvedev·Igor Chekhovskoy·Irina Vaseva·Mikhail Fedoruk
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Abstract

A fourth-order multi-exponential scheme is proposed for the Zakharov-Shabat system. The scheme represents a product of 13 exponential operators. The construction of the scheme is based on a fourth-order three-exponential scheme, which contains only one exponent with a spectral parameter. This exponent is factorized to the fourth-order with the Suzuki formula of 11 exponents. The obtained scheme allows the use of a fast algorithm in calculating the initial problem for a large number of spectral parameters and conserves the quadratic invariant exactly for real spectral parameters.

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Sergey Medvedev, Igor Chekhovskoy, Irina Vaseva, Mikhail Fedoruk. 2019-09-29. Fast Computation of the Direct Scattering Transform by Fourth Order Conservative Multi-Exponential Scheme. https://arxiv.org/abs/1909.13228

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