Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks

This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connectio...

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প্রধান লেখক: Pelinovsky, Dmitry, Noja, Diego
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ভাষা:ইংরেজি
প্রকাশিত: MDPI - Multidisciplinary Digital Publishing Institute 2021
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অনলাইন ব্যবহার করুন:42712
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author Pelinovsky, Dmitry
Noja, Diego
author_browse Noja, Diego
Pelinovsky, Dmitry
author_facet Pelinovsky, Dmitry
Noja, Diego
author_sort Pelinovsky, Dmitry
collection Directory of Open Access Books
description This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in different areas of contemporary physics with many applications in electronics, biology, material science, and nanotechnology, the development of effective modeling tools is important for the many practical problems arising in these areas. The list of important problems includes searches for standing waves, exploring of their properties (e.g., stability and asymptotic behavior), and scattering dynamics. This Special Issue is a representative sample of the works devoted to the solutions of these and other problems.
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id doab-20.500.12854ir-60378
institution Directory of Open Access Books
language eng
publishDate 2021
publishDateRange 2021
publishDateSort 2021
publisher MDPI - Multidisciplinary Digital Publishing Institute
publisherStr MDPI - Multidisciplinary Digital Publishing Institute
record_format ojs
spelling doab-20.500.12854ir-603782023-12-20T18:40:39Z Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks Pelinovsky, Dmitry Noja, Diego QA1-939 Q1-390 quantum graphs ground states open sets converging to metric graphs norm convergence of operators NLD scaling limit standing waves bound states networks localized nonlinearity nonlinear Schrödinger equation metric graphs convergence of spectra sine-Gordon equation NLS star graph point interactions Laplacians nonrelativistic limit nonlinear wave equations quantum graph soliton nonlinear shallow water equations Kre?n formula breather non-linear Schrödinger equation Schrödinger equation nodal structure bic Book Industry Communication::P Mathematics & science This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in different areas of contemporary physics with many applications in electronics, biology, material science, and nanotechnology, the development of effective modeling tools is important for the many practical problems arising in these areas. The list of important problems includes searches for standing waves, exploring of their properties (e.g., stability and asymptotic behavior), and scattering dynamics. This Special Issue is a representative sample of the works devoted to the solutions of these and other problems. 2021-02-12T05:04:05Z 2021-02-12T05:04:05Z 2019-12-09 16:10:12 2019 book 42712 9783039217212 9783039217205 https://directory.doabooks.org/handle/20.500.12854/60378 eng application/octet-stream Attribution-NonCommercial-NoDerivatives 4.0 International https://mdpi.com/books/pdfview/book/1763 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03921-721-2 10.3390/books978-3-03921-721-2 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783039217212 9783039217205 144 open access
spellingShingle QA1-939
Q1-390
quantum graphs
ground states
open sets converging to metric graphs
norm convergence of operators
NLD
scaling limit
standing waves
bound states
networks
localized nonlinearity
nonlinear Schrödinger equation
metric graphs
convergence of spectra
sine-Gordon equation
NLS
star graph
point interactions
Laplacians
nonrelativistic limit
nonlinear wave equations
quantum graph
soliton
nonlinear shallow water equations
Kre?n formula
breather
non-linear Schrödinger equation
Schrödinger equation
nodal structure
bic Book Industry Communication::P Mathematics & science
Pelinovsky, Dmitry
Noja, Diego
Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks
title Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks
title_full Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks
title_fullStr Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks
title_full_unstemmed Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks
title_short Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks
title_sort symmetries of nonlinear pdes on metric graphs and branched networks
topic QA1-939
Q1-390
quantum graphs
ground states
open sets converging to metric graphs
norm convergence of operators
NLD
scaling limit
standing waves
bound states
networks
localized nonlinearity
nonlinear Schrödinger equation
metric graphs
convergence of spectra
sine-Gordon equation
NLS
star graph
point interactions
Laplacians
nonrelativistic limit
nonlinear wave equations
quantum graph
soliton
nonlinear shallow water equations
Kre?n formula
breather
non-linear Schrödinger equation
Schrödinger equation
nodal structure
bic Book Industry Communication::P Mathematics & science
topic_facet QA1-939
Q1-390
quantum graphs
ground states
open sets converging to metric graphs
norm convergence of operators
NLD
scaling limit
standing waves
bound states
networks
localized nonlinearity
nonlinear Schrödinger equation
metric graphs
convergence of spectra
sine-Gordon equation
NLS
star graph
point interactions
Laplacians
nonrelativistic limit
nonlinear wave equations
quantum graph
soliton
nonlinear shallow water equations
Kre?n formula
breather
non-linear Schrödinger equation
Schrödinger equation
nodal structure
bic Book Industry Communication::P Mathematics & science
url 42712
work_keys_str_mv AT pelinovskydmitry symmetriesofnonlinearpdesonmetricgraphsandbranchednetworks
AT nojadiego symmetriesofnonlinearpdesonmetricgraphsandbranchednetworks