Spectrally accurate space-time solution of Manakov systems

TL;DR

This paper presents a spectrally accurate numerical method for solving Manakov systems in space and time, conserving physical invariants and validated through numerical tests.

Contribution

It introduces a novel combination of Fourier spectral methods and spectral Hamiltonian boundary value methods for Manakov systems.

Findings

High accuracy in space and time solutions

Conservation of physical invariants demonstrated

Effective numerical validation provided

Abstract

In this paper, we study the numerical solution of Manakov systems by using a spectrally accurate Fourier decomposition in space, coupled with a spectrally accurate time integration. This latter relies on the use of spectral Hamiltonian boundary Value Methods. The used approach allows to conserve all the physical invariants of the systems. Some numerical tests are reported.