Solution of High-Order Nonlinear Integrable Systems Using Darboux Transformation

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED

Axioms Pub Date : 2023-11-03 DOI:10.3390/axioms12111032

Xinhui Wu, Jiawei Hu, Ning Zhang

引用次数: 0

Abstract

The 4×4 trace-free complex matrix set is introduced in this study. By using it, we are able to create a novel soliton hierarchy that is reduced to demonstrate its bi-Hamiltonian structure. Additionally, we give the Darboux matrix T, whose elements are connected to the spectral parameter in accordance with the various positions and numbers of the spectral parameter λ. The Darboux transformation approach has also been successfully applicated to superintegrable systems.

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用达布变换求解高阶非线性可积系统

本文介绍了4×4无迹复矩阵集。通过使用它，我们能够创建一种新的孤子层次结构，并将其简化为双哈密顿结构。此外，我们给出了达布矩阵T，其元素根据光谱参数λ的不同位置和个数与光谱参数相连接。Darboux变换方法也成功地应用于超可积系统。

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

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.