Derivation of Expanded Isospectral-Nonisospectral Integrable Hierarchies via the Column-vector Loop Algebra

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI:10.1007/s10255-024-1047-1
Hai-feng Wang, Yu-feng Zhang
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引用次数: 0

Abstract

A scheme for generating nonisospectral integrable hierarchies is introduced. Based on the method, we deduce a nonisospectral hierarchy of soliton equations by considering a linear spectral problem. It follows that the corresponding expanded isospectral and nonisospectral integrable hierarchies are deduced based on a 6 dimensional complex linear space \(\widetilde{\mathbb{C}}^{6}\). By reducing these integrable hierarchies, we obtain the expanded isospectral and nonisospectral derivative nonlinear Schrödinger equation. By using the trace identity, the bi-Hamiltonian structure of these two hierarchies are also obtained. Moreover, some symmetries and conserved quantities of the resulting hierarchy are discussed.

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通过柱向量环代数推导扩展等谱-非等谱可积分层次结构
本文介绍了一种生成非异谱可积分层次结构的方法。基于该方法,我们通过考虑线性谱问题,推导出了孤子方程的非等谱层次。由此,基于 6 维复线性空间 \(\widetilde{\mathbb{C}}^{6}\)推导出相应的扩展等谱和非等谱可积分层次。通过还原这些可积分层次,我们得到了扩展的等谱和非等谱导数非线性薛定谔方程。利用迹同一性,我们还得到了这两个层次的双哈密顿结构。此外,我们还讨论了所得层次结构的一些对称性和守恒量。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
70
审稿时长
3.0 months
期刊介绍: Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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