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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Year of Publication: | 2019 |
Language: | English |
Physical Description: | 1 electronic resource (144 p.) |
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(CKB)4100000010106232 (oapen)https://directory.doabooks.org/handle/20.500.12854/60378 (EXLCZ)994100000010106232 |
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Pelinovsky, Dmitry auth Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks MDPI - Multidisciplinary Digital Publishing Institute 2019 1 electronic resource (144 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier 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. English 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 3-03921-720-8 Noja, Diego auth |
language |
English |
format |
eBook |
author |
Pelinovsky, Dmitry |
spellingShingle |
Pelinovsky, Dmitry Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks |
author_facet |
Pelinovsky, Dmitry Noja, Diego |
author_variant |
d p dp |
author2 |
Noja, Diego |
author2_variant |
d n dn |
author_sort |
Pelinovsky, Dmitry |
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_auth |
Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks |
title_new |
Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks |
title_sort |
symmetries of nonlinear pdes on metric graphs and branched networks |
publisher |
MDPI - Multidisciplinary Digital Publishing Institute |
publishDate |
2019 |
physical |
1 electronic resource (144 p.) |
isbn |
3-03921-721-6 3-03921-720-8 |
illustrated |
Not Illustrated |
work_keys_str_mv |
AT pelinovskydmitry symmetriesofnonlinearpdesonmetricgraphsandbranchednetworks AT nojadiego symmetriesofnonlinearpdesonmetricgraphsandbranchednetworks |
status_str |
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(CKB)4100000010106232 (oapen)https://directory.doabooks.org/handle/20.500.12854/60378 (EXLCZ)994100000010106232 |
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Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks |
author2_original_writing_str_mv |
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