Positive low-action solutions of the NLS on graphs with terminal edges concentrate on a terminal edge at large frequencies as rescaled real-line solitons, and Lyapunov-Schmidt reduction constructs one- and multi-peaked solutions exploiting those edges.
Mass-constrained ground states of the stationary NLSE on periodic metric graphs
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We investigate the existence of ground states with fixed mass for the nonlinear Schr\"odinger equation with a pure power nonlinearity on periodic metric graphs. Within a variational framework, both the $L^2$-subcritical and critical regimes are studied. In the former case, we establish the existence of global minimizers of the NLS energy for every mass and every periodic graph. In the critical regime, a complete topological characterization is derived, providing conditions which allow or prevent ground states of a certain mass from existing. Besides, a rigorous notion of periodic graph is introduced and discussed.
fields
math.AP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Peaked and low action solutions of NLS equations on graphs with terminal edges
Positive low-action solutions of the NLS on graphs with terminal edges concentrate on a terminal edge at large frequencies as rescaled real-line solitons, and Lyapunov-Schmidt reduction constructs one- and multi-peaked solutions exploiting those edges.