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.
Anal.70 (2010), 199–230
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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.