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首页> 外文期刊>PHYSICAL REVIEW E >Stability boundary and collisions of two-dimensional solitons in PT -symmetric couplers with the cubic-quintic nonlinearity
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Stability boundary and collisions of two-dimensional solitons in PT -symmetric couplers with the cubic-quintic nonlinearity

机译：具有三次立方非线性的PT对称耦合器中二维孤子的稳定性边界和碰撞

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摘要

We introduce one- and two-dimensional (1D and 2D) models of parity-time (PT )-symmetric couplers withnthe mutually balanced linear gain and loss applied to the two cores and cubic-quintic (CQ) nonlinearity actingnin each one. The 2D and 1D models may be realized in dual-core optical wave guides in the spatiotemporalnand spatial domains, respectively. Stationary solutions for PT -symmetric solitons in these systems reduce tontheir counterparts in the usual coupler. The most essential problem is the stability of the solitons, which becomenunstable against symmetry breaking with the increase of the energy (norm) and retrieve the stability at still largernenergies. The boundary value of the intercore-coupling constant, above which the solitons are completely stable,nis found by means of an analytical approximation, based on the cw (zero-dimensional) counterpart of the system.nThe approximation demonstrates good agreement with numerical findings for the 1D and 2D solitons. Numericalnresults for the stability limits of the 2D solitons are obtained bymeans of the computation of eigenvalues for smallnperturbations, and verified in direct simulations. Although large parts of the soliton families are unstable, theninstability is quite weak. Collisions between 2D solitons in the PT -symmetric coupler are studied by means ofnsimulations. Outcomes of the collisions are inelastic but not destructive, as they do not break the PT symmetry.
机译：我们介绍了奇偶时间（PT）对称耦合器的一维和二维（1D和2D）模型，将相互平衡的线性增益和损耗应用到两个磁芯上，并且分别应用了三次立方（CQ）非线性。 2D和1D模型可以分别在时空域和空间域中在双核光波导中实现。这些系统中PT对称孤子的固定解决方案减少了常规耦合器中相应部件的数量。最本质的问题是孤子的稳定性，随着能量（范数）的增加，对称子对于对称性的破坏变得无能为力，而在更大的能量下恢复稳定性。核间耦合常数的边界值，在该边界值上，孤子是完全稳定的，它是基于系统的cw（零维）对应物，通过解析近似法找到的。一维和二维孤子。通过计算小扰动特征值的方法获得了二维孤子稳定性极限的数值结果，并在直接仿真中进行了验证。尽管孤子族的大部分都是不稳定的，但是不稳定是相当弱的。通过仿真研究了PT对称耦合器中二维孤子之间的碰撞。碰撞的结果是无弹性的，但不是破坏性的，因为它们不会破坏PT的对称性。

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  • 来源
    《PHYSICAL REVIEW E》 |2013年第6期|1-8|共8页
  • 作者

    Gennadiy Burlak; Boris A. Malomed;

  • 作者单位

    Centro de Investigaci´on en Ingenier´ıa y Ciencias Aplicadas Universidad Aut´onoma del Estado de Morelos Cuernavaca Morelos M´exico;

    Department of Physical Electronics School of Electric Engineering Faculty of Engineering Tel Aviv University Tel Aviv 69978 Israel;

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