Fast Computation of the Direct Scattering Transform by Fourth Order Conservative Multi-Exponential Scheme
Numerical Analysis
2019-10-01 v1 Numerical Analysis
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1909.13228,
title = {Fast Computation of the Direct Scattering Transform by Fourth Order Conservative Multi-Exponential Scheme},
author = {Sergey Medvedev and Igor Chekhovskoy and Irina Vaseva and Mikhail Fedoruk},
journal= {arXiv preprint arXiv:1909.13228},
year = {2019}
}