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Time-Independent Nonlinear Schrödinger Equation on Simplest Networks

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Low-Dimensional Functional Materials

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Abstract

We treat the time-independent (cubic) nonlinear Schrödinger equation (NLSE) on simplest networks. In particular, the solutions are obtained for star and tree graphs with the boundary conditions providing vertex matching and flux conservation. It is shown that the method can be extended to the case of arbitrary number of bonds in star graphs and for other simplest topologies.

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Author information

Authors and Affiliations

  1. Department of Physics, National University of Uzbekistan, Tashkent, Uzbekistan

    Karimjon Sabirov

  2. Department of Energy, Turin Polytechnic University in Tashkent, Tashkent, Uzbekistan

    Zarif Sabirov & Donyor Babajanov

  3. Department of Energy, Laboratory for Advanced Studies, Turin Polytechnic University in Tashkent, Tashkent, Uzbekistan

    Davron Matrasulov

Authors
  1. Karimjon Sabirov
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  2. Zarif Sabirov
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  3. Donyor Babajanov
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  4. Davron Matrasulov
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Corresponding author

Correspondence to Karimjon Sabirov .

Editor information

Editors and Affiliations

  1. , Institut für Theoretische Physik IV, Heinrich-Heine-Universität, Universitätsstrasse 1, Düsseldorf, 40225, Germany

    Reinhold Egger

  2. Laboratory for Advanced Studies, Department of Energy, Turin Polytechnic University in Tashkent, Niyazov St. 17, Tashkent, 100174, Uzbekistan

    Davron Matrasulov

  3. , Department of Physics, National University of Uzbekistan, Niyazov St. 17, Tashkent, 100174, Uzbekistan

    Khamdam Rakhimov

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Sabirov, K., Sabirov, Z., Babajanov, D., Matrasulov, D. (2013). Time-Independent Nonlinear Schrödinger Equation on Simplest Networks. In: Egger, R., Matrasulov, D., Rakhimov, K. (eds) Low-Dimensional Functional Materials. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6618-1_13

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