孤子解理论中的二元论

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Computational Mathematics and Mathematical Physics Pub Date : 2024-09-01 DOI:10.1134/s0965542524700581

L. A. Beklaryan, A. L. Beklaryan

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引用次数: 0

摘要

摘要讨论了孤子解理论与点式函数微分方程解理论的二元对立。我们描述了这种二元对立的形式基础，其核心要素是孤子束概念以及 "函数-操作符 "二元对立。在这种方法的框架内，可以描述具有给定特征的孤子解的整个空间及其在空间和时间上的渐近性。例如，曼哈顿晶格上的交通流模型就是用来描述整个有界孤子解的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Dualism in the Theory of Soliton Solutions

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Dualism in the Theory of Soliton Solutions

Abstract

The dualism of the theories of soliton solutions and solutions to functional differential equations of pointwise type is discussed. We describe the foundations underlying the formalism of this dualism, the central element of which is the concept of a soliton bouquet, as well as a dual pair “function–operator.” Within the framework of this approach, it is possible to describe the entire space of soliton solutions with a given characteristic and their asymptotics in both space and time. As an example, the model of traffic flow on the Manhattan lattice is used to describe the whole family of bounded soliton solutions.

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来源期刊

Computational Mathematics and Mathematical Physics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.50

自引率

14.30%

发文量

125

审稿时长

4-8 weeks

期刊介绍： Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.