## View abstract

### Session S22 - Deterministic and probabilistic aspects of nonlinear evolution equations

Thursday, July 22, 16:35 ~ 17:05 UTC-3

## Instability of soliton-type profiles on metric graphs

### Jaime Angulo Pava

In this talk we shed new light on the mathematical studies of nonlinear dispersive evolution equations on metric graphs. This trend has been mainly motivated by the demand of reliable mathematical models for diferent phenomena in branched systems which, in meso- or nano-scales, resemble a thin neighborhood of a graph, such as Josephson junction networks, electric circuits, blood pressure waves in large arteries, or nerve impulses in complex arrays of neurons, just to mention a few examples. Our dynamic problems here will be essentially related to the sine-Gordon model on a $\mathcal Y$-junction graph. We establish a general linear instability criterium for solitons profiles associated to nonlinear dispersive evolution equations on metric graphs. In particular, we see that some kink or kink/anti-kink soliton profiles for the sine-Gordon model are linearly (and nonlinearly) unstable.