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...
সংরক্ষণ করুন:
| প্রধান লেখক: | , |
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| বিন্যাস: | Online |
| ভাষা: | ইংরেজি |
| প্রকাশিত: |
MDPI - Multidisciplinary Digital Publishing Institute
2021
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | 42712 |
| ট্যাগগুলো: |
কোনো ট্যাগ নেই, প্রথমজন হিসাবে ট্যাগ করুন!
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| _version_ | 1869528456956477440 |
|---|---|
| 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. |
| format | Online |
| 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 |