Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks

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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Bibliographic Details
Main Author: Pelinovsky, Dmitry (auth)
Other Authors: Noja, Diego (auth)
Format: Electronic Book Chapter
Language:English
Published: MDPI - Multidisciplinary Digital Publishing Institute 2019
Subjects:
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
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Summary: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.
Physical Description:1 electronic resource (144 p.)
ISBN:books978-3-03921-721-2
9783039217212
9783039217205
Access:Open Access

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