New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem

For the spatially-distributed Fermi–Pasta–Ulam (FPU) equation, irregular solutions are studied that contain components rapidly oscillating in the spatial variable, with different asymptotically large modes. The main result of this paper is the construction of families of special nonlinear systems of...

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Autores principales:	Sergey Kashchenko, Anna Tolbey
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Fermi–Pasta–Ulam problem quasinormal forms asymptotics special distributed chains Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/44f44441fc0f4f6da3aaa859f6de6a8e
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spelling	oai:doaj.org-article:44f44441fc0f4f6da3aaa859f6de6a8e2021-11-25T18:16:46ZNew Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem10.3390/math92228722227-7390https://doaj.org/article/44f44441fc0f4f6da3aaa859f6de6a8e2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2872https://doaj.org/toc/2227-7390For the spatially-distributed Fermi–Pasta–Ulam (FPU) equation, irregular solutions are studied that contain components rapidly oscillating in the spatial variable, with different asymptotically large modes. The main result of this paper is the construction of families of special nonlinear systems of the Schrödinger type—quasinormal forms—whose nonlocal dynamics determines the local behavior of solutions to the original problem, as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. On their basis, results are obtained on the asymptotics in the main solution of the FPU equation and on the interaction of waves moving in opposite directions. The problem of “perturbing” the number of <i>N</i> elements of a chain is considered. In this case, instead of the differential operator, with respect to one spatial variable, a special differential operator, with respect to two spatial variables appears. This leads to a complication of the structure of an irregular solution.Sergey KashchenkoAnna TolbeyMDPI AGarticleFermi–Pasta–Ulam problemquasinormal formsasymptoticsspecial distributed chainsMathematicsQA1-939ENMathematics, Vol 9, Iss 2872, p 2872 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Fermi–Pasta–Ulam problem quasinormal forms asymptotics special distributed chains Mathematics QA1-939
spellingShingle	Fermi–Pasta–Ulam problem quasinormal forms asymptotics special distributed chains Mathematics QA1-939 Sergey Kashchenko Anna Tolbey New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem
description	For the spatially-distributed Fermi–Pasta–Ulam (FPU) equation, irregular solutions are studied that contain components rapidly oscillating in the spatial variable, with different asymptotically large modes. The main result of this paper is the construction of families of special nonlinear systems of the Schrödinger type—quasinormal forms—whose nonlocal dynamics determines the local behavior of solutions to the original problem, as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. On their basis, results are obtained on the asymptotics in the main solution of the FPU equation and on the interaction of waves moving in opposite directions. The problem of “perturbing” the number of <i>N</i> elements of a chain is considered. In this case, instead of the differential operator, with respect to one spatial variable, a special differential operator, with respect to two spatial variables appears. This leads to a complication of the structure of an irregular solution.
format	article
author	Sergey Kashchenko Anna Tolbey
author_facet	Sergey Kashchenko Anna Tolbey
author_sort	Sergey Kashchenko
title	New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem
title_short	New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem
title_full	New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem
title_fullStr	New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem
title_full_unstemmed	New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem
title_sort	new irregular solutions in the spatially distributed fermi–pasta–ulam problem
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/44f44441fc0f4f6da3aaa859f6de6a8e
work_keys_str_mv	AT sergeykashchenko newirregularsolutionsinthespatiallydistributedfermipastaulamproblem AT annatolbey newirregularsolutionsinthespatiallydistributedfermipastaulamproblem
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New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem

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