# Networks with point like nonlinearities

## TL;DR

This paper investigates static nonlinear waves in network structures modeled by a nonlinear Schrödinger equation with point-like nonlinearities, deriving explicit solutions and discovering spontaneous symmetry breaking due to bifurcations.

## Contribution

It provides explicit solutions for nonlinear waves on metric graphs with point-like nonlinearities and analyzes symmetry-breaking bifurcations, advancing understanding of nonlinear wave behavior in networks.

## Key findings

- Explicit solutions satisfying vertex boundary conditions.
- Identification of spontaneous symmetry breaking caused by bifurcations.
- Insights into nonlinear wave dynamics on network structures.

## Abstract

We study static nonlinear waves in networks described by a nonlinear Schrodinger equation with point-like nonlinearities on metric graphs. Explicit solutions fulfilling vertex boundary conditions are obtained. Spontaneous symmetry breaking caused by bifurcations is found.