LEADER 03144nam 2200637z- 450 001 9910367748503321 005 20231214133339.0 010 $a3-03921-721-6 035 $a(CKB)4100000010106232 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/60378 035 $a(EXLCZ)994100000010106232 100 $a20202102d2019 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSymmetries of Nonlinear PDEs on Metric Graphs and Branched Networks 210 $cMDPI - Multidisciplinary Digital Publishing Institute$d2019 215 $a1 electronic resource (144 p.) 311 $a3-03921-720-8 330 $aThis 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. 610 $aquantum graphs 610 $aground states 610 $aopen sets converging to metric graphs 610 $anorm convergence of operators 610 $aNLD 610 $ascaling limit 610 $astanding waves 610 $abound states 610 $anetworks 610 $alocalized nonlinearity 610 $anonlinear Schrödinger equation 610 $ametric graphs 610 $aconvergence of spectra 610 $asine-Gordon equation 610 $aNLS 610 $astar graph 610 $apoint interactions 610 $aLaplacians 610 $anonrelativistic limit 610 $anonlinear wave equations 610 $aquantum graph 610 $asoliton 610 $anonlinear shallow water equations 610 $aKre?n formula 610 $abreather 610 $anon-linear Schrödinger equation 610 $aSchrödinger equation 610 $anodal structure 700 $aPelinovsky$b Dmitry$4auth$0477390 702 $aNoja$b Diego$4auth 906 $aBOOK 912 $a9910367748503321 996 $aSymmetries of Nonlinear PDEs on Metric Graphs and Branched Networks$93023454 997 $aUNINA