najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-1-29-37najo-726Research ArticleMATHEMATICSМАТЕМАТИКАNonlinear standing waves on planar branched systems: shrinking into metric graphSobirovZ.

60A, Amir Temur Str., 100000, Tashkent

sobirovzar@gmail.comBabajanovD.

17 Niyazov Str., 100095, Tashkent

MatrasulovD.

17 Niyazov Str., 100095, Tashkent

Tashkent Financial InstituteUzbekistanTurin Polytechnic University in TashkentUzbekistan201713082025812937Copyright © Sobirov Z., Babajanov D., Matrasulov D., 20252025Sobirov Z., Babajanov D., Matrasulov D.Sobirov Z., Babajanov D., Matrasulov D.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/726

We treat the stationary nonlinear Schrӧdinger equation on two-dimensional branched domains, so-called fat graphs. The shrinking limit when the domain becomes one-dimensional metric graph is studied by using analytical estimate of the convergence of fat graph boundary conditions into those for metric graph. Detailed analysis of such convergence on the basis of numerical solution of stationary nonlinear Schrӧdinger equation on a fat graph is provided. The possibility for reproducing different metric graph boundary conditions studied in earlier works is shown. Practical applications of the proposed model for such problems as Bose-Einstein condensation in networks, branched optical media, DNA, conducting polymers and wave dynamics in branched capillary networks are discussed.

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The authors declare that there are no conflicts of interest present.