组合导数非线性薛定谔孤子层次结构

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-06-01 DOI:10.1016/S0034-4877(24)00040-5

Wen-Xiu Ma

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引用次数: 0

摘要

本文旨在基于特定的矩阵李代数，研究一个具有四个势的考普-纽厄尔（Kaup-Newell）型矩阵特征值问题，并在零曲率公式中构建一个相关的组合导数非线性薛定谔（NLS）方程的孤子层次结构。通过探索其遗传递归算子和双哈密顿公式，证明了所得到的孤子层次结构的Liouville可积分性。第一个非线性实例提供了一个可积分模型，该模型由具有两个任意常数的组合导数 NLS 方程组成。

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A combined derivative nonlinear SchrÖdinger soliton hierarchy

This paper aims to study a Kaup-Newell type matrix eigenvalue problem with four potentials, based on a specific matrix Lie algebra, and construct an associated soliton hierarchy of combined derivative nonlinear Schrödinger (NLS) equations, within the zero curvature formulation. The Liouville integrability of the resulting soliton hierarchy is shown by exploring its hereditary recursion operator and bi-Hamiltonian formulation. The first nonlinear example provides an integrable model consisting of combined derivative NLS equations with two arbitrary constants.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.