Fokker–Planck equation on metric graphs

Bogoliubov-de Gennes equation on graphs: A model for tree-branched Majorana wire network

“…For modeling of nonlinear waves and soliton dynamics in branched structures one should consider nonlinear wave equations on metric graphs. During the past decade the studies of particle and wave dynamics in branched structures have been extended to nonlinear evolution equations by considering nonlinear Schrödinger and sine-Gordon equations on metric graphs [22]- [33]. For such equations, one should derive the vertex boundary conditions from fundamental conservation laws such as energy, momentum, charge and mass conservation [22,31].…”