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

## TL;DR

This paper introduces a new fourth-order numerical algorithm for solving the Zakharov-Shabat spectral problem, improving accuracy and efficiency over existing methods for continuous and discrete spectra.

## Contribution

The paper presents a novel high-precision, fourth-order algorithm that generalizes the Boffetta-Osborne scheme for the Zakharov-Shabat problem.

## Key findings

- Achieves fourth-order accuracy in solving the Zakharov-Shabat system
- Enhances efficiency in spectral problem computations
- Applicable to both continuous and discrete spectra

## 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.