Zegadlo Krzysztof, Dror Nir, Viet Hung Nguyen, Trippenbach Marek, Malomed Boris A
Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warszawa, Poland.
Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland.
Phys Rev E. 2017 Jul;96(1-1):012204. doi: 10.1103/PhysRevE.96.012204. Epub 2017 Jul 5.
We report results of systematic analysis of various modes in the flatband lattice, based on the diamond-chain model with the on-site cubic nonlinearity, and its double version with the linear on-site mixing between the two lattice fields. In the single-chain system, a full analysis is presented, first, for the single nonlinear cell, making it possible to find all stationary states, viz., antisymmetric, symmetric, and asymmetric ones, including an exactly investigated symmetry-breaking bifurcation of the subcritical type. In the nonlinear infinite single-component chain, compact localized states (CLSs) are found in an exact form too, as an extension of known compact eigenstates of the linear diamond chain. Their stability is studied by means of analytical and numerical methods, revealing a nontrivial stability boundary. In addition to the CLSs, various species of extended states and exponentially localized lattice solitons of symmetric and asymmetric types are also studied, by means of numerical calculations and variational approximation. As a result, existence and stability areas are identified for these modes. Finally, the linear version of the double diamond chain is solved in an exact form, producing two split flatbands in the system's spectrum.
我们报告了基于具有在位立方非线性的金刚石链模型及其两个晶格场之间具有线性在位混合的双版本模型，对平带晶格中各种模式进行系统分析的结果。在单链系统中，首先对单个非线性单元进行了全面分析，从而有可能找到所有稳态，即反对称、对称和非对称稳态，包括对亚临界类型的精确研究的对称破缺分岔。在非线性无限单组分链中，紧致局域态（CLSs）也以精确形式被找到，作为线性金刚石链已知紧致本征态的扩展。通过解析和数值方法研究了它们的稳定性，揭示了一个非平凡的稳定性边界。除了CLSs，还通过数值计算和变分近似研究了各种类型的扩展态以及对称和非对称类型的指数局域晶格孤子。结果，确定了这些模式的存在和稳定区域。最后，以精确形式求解了双金刚石链的线性版本，在系统频谱中产生了两个分裂的平带。
