{"title":"Numerical Methods for Constructing Solutions of Functional Differential Equations of Pointwise Type","authors":"Beklaryan Armen","doi":"10.25728/ASSA.2020.20.2.878","DOIUrl":null,"url":null,"abstract":"The article discusses construction of traveling wave type solutions for the FrenkelKontorova model on the propagation of longitudinal waves. For the first time, based on the existence and uniqueness theorem of traveling wave type solutions, as well as the approximation theorem, a complete family of traveling wave type solutions is constructed in the form of subfamilies of bounded solutions (horizontals) and unbounded solutions (verticals).","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"20 1","pages":"56-70"},"PeriodicalIF":0.0000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Systems Science and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.25728/ASSA.2020.20.2.878","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 2
Abstract
The article discusses construction of traveling wave type solutions for the FrenkelKontorova model on the propagation of longitudinal waves. For the first time, based on the existence and uniqueness theorem of traveling wave type solutions, as well as the approximation theorem, a complete family of traveling wave type solutions is constructed in the form of subfamilies of bounded solutions (horizontals) and unbounded solutions (verticals).
期刊介绍：
Advances in Systems Science and Applications (ASSA) is an international peer-reviewed open-source online academic journal. Its scope covers all major aspects of systems (and processes) analysis, modeling, simulation, and control, ranging from theoretical and methodological developments to a large variety of application areas. Survey articles and innovative results are also welcome. ASSA is aimed at the audience of scientists, engineers and researchers working in the framework of these problems. ASSA should be a platform on which researchers will be able to communicate and discuss both their specialized issues and interdisciplinary problems of systems analysis and its applications in science and industry, including data science, artificial intelligence, material science, manufacturing, transportation, power and energy, ecology, corporate management, public governance, finance, and many others.
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