Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system in optical applications

Abstract

Based on the generalized Cayley transform, a family of conservative one-step schemes of the sixth order of accuracy for the Zakharov-Shabat system is constructed. The exponential integrator is a special case. Schemes based on rational approximation allow the use of fast algorithms to solve the initial problem for a large number of values of the spectral parameter.

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