Preprint

Transparent PT-symmetric nonlinear networks

M. AkramovNational University of Uzbekistan , Universitet Str. 4 , 100174 , Tashkent , UzbekistanJambul YusupovKimyo Int. University in Tashkent , 156 Usman Nasyr Str. , 100121 , Tashkent , UzbekistanMatthias EhrhardtBergische Universität Wuppertal , Gaußstrasse 20 , D-42119 Wuppertal , GermanyH. SusantoKhalifa University , 127788 , Abu Dhabi , United Arab EmiratesD. U. MatrasulovTurin Polytechnic University in Tashkent , 17 Niyazov Str. , 100095 , Tashkent , Uzbekistan

2024en

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ABI

Annotatsiya

We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schrödinger (NNLS) equation on metric graphs, for which transparent boundary conditions are imposed at the vertices. By employing the ``potential approach" previously used for the nonlinear Schrödinger equation, we derive transparent boundary conditions for the NNLS equation on metric graphs. These conditions eliminate backscattering at graph vertices, which is crucial for minimizing losses in signal, heat, and charge transfer in various applications such as optical fibers, optoelectronic networks, and low-dimensional materials.

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DOI: 10.48550/arxiv.2408.03709

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