Konotop V V, Takeno S
Department of Physics and Center of Mathematical Sciences, University of Madeira, Praça do Município, Funchal P-9000, Portugal.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jul;60(1):1001-8. doi: 10.1103/physreve.60.1001.
Various kinds of stationary dark localized modes in discrete nonlinear Schrödinger equations are considered. A criterion for the existence of such excitations is introduced and an estimation of a localization region is provided. The results are illustrated in examples of the deformable discrete nonlinear Schrödinger equation, of the model of Frenkel excitons in a chain of two-level atoms, and of the model of a one-dimensional Heisenberg ferromagnetic in the stationary phase approximation. The three models display essentially different properties. It is shown that at an arbitrary amplitude of the background it is impossible to reach strong localization of dark modes. In the meantime, in the model of Frenkel excitons, exact dark compacton solutions are found.
考虑了离散非线性薛定谔方程中的各种稳态暗局域模。引入了此类激发存在的判据，并给出了局域区域的估计。通过可变形离散非线性薛定谔方程、两能级原子链中弗伦克尔激子模型以及稳态相位近似下一维海森堡铁磁体模型的例子对结果进行了说明。这三个模型表现出本质上不同的性质。结果表明，在任意背景振幅下，都不可能实现暗模的强局域化。同时，在弗伦克尔激子模型中找到了精确的暗紧致子解。
