标题： 两组分超材料和光子晶体模型中的单峰和多峰孤子 显示英文标题

标题： Single- and multi-peak solitons in two-component models of metamaterials and photonic crystals

摘要： 我们报告了关于在由XPM相互作用耦合的两个非线性薛定谔（NLS）方程系统中孤子的研究结果，该模型模拟了两种波在超材料（MMs）中的共传播。 同样的模型也适用于光子晶体（PCs），以及接近零色散点的普通光纤。 该系统的特殊之处在于其中一个方程的相对群速度色散（GVD）系数具有小的正或负值，而另一个方程的色散为异常。 与之前研究的具有相等GVD系数的非线性耦合NLS方程系统不同，后者仅产生简单的单峰孤子，而本模型产生了具有复杂形状的孤子族，这些孤子在中心处具有扩展的振荡尾部和/或双峰结构。 确定了单峰和双峰双模孤子的存在区域，展示了系统中的广泛双稳态。 在存在边界之后，它们退化为单组分解。 直接模拟表明孤子在整个存在区域内是稳定的。 还考虑了群速度失配（GVM）和光学损耗的影响。 证明可以通过相应的“管理”方案使孤子稳定以对抗GVM。 在损耗的作用下，孤子的复杂形状退化为简单形状，但周期性补偿损耗可以维持复杂性。 显示英文摘要

摘要： We report results of the study of solitons in a system of two nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials(MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations with equal GVD coefficients, which generate only simple single-peak solitons, the present model gives rise to families of solitons with complex shapes, which feature extended oscillatory tails and/or a double-peak structure at the center. Regions of existence are identified for single- and double-peak bimodal solitons, demonstrating a broad bistability in the system. Behind the existence border, they degenerate into single-component solutions. Direct simulations demonstrate stability of the solitons in the entire existence regions. Effects of the group-velocity mismatch (GVM) and optical loss are considered too. It is demonstrated that the solitons can be stabilized against the GVM by means of the respective "management" scheme. Under the action of the loss, complex shapes of the solitons degenerate into simple ones, but periodic compensation of the loss supports the complexity.