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arXiv · 1901.02696

An overview on the standing waves of nonlinear Schr\"odinger and Dirac equations on metric graphs with localized nonlinearity

William Borrelli·Raffaele Carlone·Lorenzo Tentarelli
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Abstract

We present a brief overview on the existence/nonexistence of standing waves for the NonLinear Schr\"odinger and the NonLinear Dirac Equations (NLSE/NLDE) on metric graphs with localized nonlinearity. We first focus on the NLSE, both in the subcritical and the critical case, and then on the NLDE, highlighting similarities and differences with the NLSE. Finally, we show how the two equations are related in the nonrelativistic limit, proving the convergence of bound states.

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William Borrelli, Raffaele Carlone, Lorenzo Tentarelli. 2019-01-09. An overview on the standing waves of nonlinear Schr\"odinger and Dirac equations on metric graphs with localized nonlinearity. https://doi.org/10.3390/sym11020169

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