Akramov M, Sabirov K, Matrasulov D, Susanto H, Usanov S, Karpova O
Physics Department, National University of Uzbekistan, Vuzgorodok, Tashkent 100174, Uzbekistan.
Tashkent University of Information Technology, Amir Temur Avenue 108, Tashkent 100200, Uzbekistan.
Phys Rev E. 2022 May;105(5-1):054205. doi: 10.1103/PhysRevE.105.054205.
We consider the parity-time (PT)-symmetric, nonlocal, nonlinear Schrödinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. Soliton solutions are obtained for the simplest graph topologies, such as star and tree graphs. The integrability of the problem is shown by proving the existence of an infinite number of conservation laws. A model for soliton generation in such PT-symmetric optical fibers and their networks governed by the nonlocal nonlinear Schrödinger equation is proposed. Exact formulas for the number of generated solitons are derived for the cases when the problem is integrable. Numerical solutions are obtained for the case when integrability is broken.
我们考虑度量图上的宇称时间（PT）对称、非局部、非线性薛定谔方程。顶点边界条件由守恒定律导出。对于最简单的图拓扑结构，如星形图和树形图，得到了孤子解。通过证明存在无穷多个守恒定律，表明了该问题的可积性。提出了一个由非局部非线性薛定谔方程控制的此类PT对称光纤及其网络中孤子产生的模型。对于问题可积的情况，推导了产生孤子数目的精确公式。对于可积性被破坏的情况，得到了数值解。
