Published January 1, 2023
| Version v1
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Discrete nonlocal nonlinear Schrodinger equation on graphs: Dynamics of PT-symmetric solitons in discrete networks
Creators
- 1. Natl Univ Uzbekistan, 4 Univ Str, Tashkent 100174, Uzbekistan
- 2. Navoi State Min Inst, 27 Janubiy Str, Navoi 210100, Uzbekistan
- 3. Turin Polytech Univ Tashkent, 17 Niyazov Str, Tashkent 100095, Uzbekistan
Description
We consider discrete nonlocal nonlinear Schrodinger equation proposed earlier by Ablowitz and Musslimani, on a branched 1D lattice, presented in terms of the graphs with discrete bonds. The soliton solutions are derived for some simplest (star and tree) graphs. Numerical solutions are obtained for the cases, when the problem does not approve the analytical one. Integrability of the problem is shown by proving existence of infinite number of conservation laws.(c) 2022 Elsevier B.V. All rights reserved.
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