On the combined method for solving the inverse problem of the Zakharov–Shabat system

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-09-22 DOI:10.1016/j.physd.2025.134942

S.B. Medvedev , I.A. Vaseva , M.P. Fedoruk

引用次数: 0

Abstract

We study the combined method for solving the inverse problem of the Zakharov–Shabat system associated with the nonlinear Schrödinger equation. The method is based on a high-precision algorithm for the Gelfand–Levitan–Marchenko equation for a continuous spectrum and the Darboux method for a discrete spectrum. A comparison of the combined Darboux method and the GLME-based algorithm is made.

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求解Zakharov-Shabat系统逆问题的组合方法

研究了求解非线性Schrödinger方程的Zakharov-Shabat方程组逆问题的组合方法。该方法基于连续谱的Gelfand-Levitan-Marchenko方程的高精度算法和离散谱的Darboux方法。将Darboux法与基于glme的算法进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.