Abstract | Keywords | Export | Availability | Bookmark

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

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