Novel Numerical Algorithm with Fourth-Order Accuracy for the Direct Zakharov-Shabat Problem

Abstract

We propose a new high-precision algorithm for solving the initial problem for the Zakharov-Shabat system. This method has the fourth order of accuracy and is a generalization of the second order Boffetta-Osborne scheme. It is allowed by our method to solve more effectively the Zakharov-Shabat spectral problem for continuous and discrete spectra.

References in corpus (2)

• Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation
• Higher Order Convergent Fast Nonlinear Fourier Transform

Cited by in corpus (3)

• Exponential Fourth Order Schemes for Direct Zakharov-Shabat problem
• Direct scattering transform: catch soliton if you can
• Efficient Nonlinear Fourier Transform Algorithms of Order Four on Equispaced Grid