Sala Seminari (Dip. Matematica).<\/p>\n
Nonlinear dynamics on graphs has rapidly become a topical issue with many physical applications, ranging from nonlinear optics to Bose\u2013Einstein condensation. In the first part of the talk, we introduce the problem of the existence of ground states at fixed mass for a focusing nonlinear Schr\u00f6dinger equation with a standard nonlinearity of power type, highlighting how the topology of the graph can affect the existence results. In the second part, we study the same minimization problem for a nonlinear Schr\u00f6dinger equation with two focusing power\u2013type nonlinear terms: a pointwise one, located at the vertices of the graph, and a standard one. We show that existence and non\u2013existence results strongly depend on the interplay between the two nonlinearities and on the topological and metric properties of the graph. Link to attend remotely and form to attend in presence available at: https:\/\/seminarimap.wixsite.com\/seminarimap\/2021-2022\/filippo-boni <\/p>\n","protected":false},"excerpt":{"rendered":"
Nonlinear dynamics on graphs has rapidly become a topical issue with many physical applications, ranging from nonlinear optics to Bose\u2013Einstein condensation. In the first part of the talk, we introduce the problem of the existence of ground states…<\/p>\n