{"title":"Dualism in the Theory of Soliton Solutions","authors":"L. A. Beklaryan, A. L. Beklaryan","doi":"10.1134/s0965542524700581","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":"10 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700581","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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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.
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.
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