广义因费尔德-罗兰兹方程的守恒定律和局部哈密顿结构的不存在性

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)00038-7

Jakub Vašíček

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引用次数: 0

摘要

对于 Infeld-Rowlands 方程的某一自然广义化，我们证明了任意阶的非三维局部哈密顿结构和非三维局部交映结构，以及任意阶的非三维局部诺特算子和非三维局部逆诺特算子的不存在性，并详尽地描述了当有关方程承认任意阶的非三维局部守恒定律时的所有情况；建立上述不存在性结果的方法可方便地应用于许多其他 PDEs。

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Conservation laws and nonexistence of local Hamiltonian structures for generalized Infeld—Rowlands equation

For a certain natural generalization of the Infeld—Rowlands equation we prove nonexistence of nontrivial local Hamiltonian structures and nontrivial local symplectic structures of any order, as well as of nontrivial local Noether and nontrivial local inverse Noether operators of any order, and exhaustively characterize all cases when the equation in question admits nontrivial local conservation laws of any order; the method of establishing the above nonexistence results can be readily applied to many other PDEs.

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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.