Burlak Gennadiy, Malomed Boris A
Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Cuernavaca, Morelos, México.
Department of Physical Electronics, School of Electric Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):062904. doi: 10.1103/PhysRevE.88.062904. Epub 2013 Dec 3.
We introduce one- and two-dimensional (1D and 2D) models of parity-time (PT)-symmetric couplers with the mutually balanced linear gain and loss applied to the two cores and cubic-quintic (CQ) nonlinearity acting in each one. The 2D and 1D models may be realized in dual-core optical wave guides in the spatiotemporal and spatial domains, respectively. Stationary solutions for PT-symmetric solitons in these systems reduce to their counterparts in the usual coupler. The most essential problem is the stability of the solitons, which become unstable against symmetry breaking with the increase of the energy (norm) and retrieve the stability at still larger energies. The boundary value of the intercore-coupling constant, above which the solitons are completely stable, is found by means of an analytical approximation, based on the cw (zero-dimensional) counterpart of the system. The approximation demonstrates good agreement with numerical findings for the 1D and 2D solitons. Numerical results for the stability limits of the 2D solitons are obtained by means of the computation of eigenvalues for small perturbations, and verified in direct simulations. Although large parts of the soliton families are unstable, the instability is quite weak. Collisions between 2D solitons in the PT-symmetric coupler are studied by means of simulations. Outcomes of the collisions are inelastic but not destructive, as they do not break the PT symmetry.
我们引入了奇偶时间（PT）对称耦合器的一维和二维（1D和2D）模型，其中两个芯分别施加相互平衡的线性增益和损耗，并在每个芯中存在立方-五次（CQ）非线性。二维和一维模型可分别在时空域和空间域的双核光波导中实现。这些系统中PT对称孤子的定态解简化为普通耦合器中的对应解。最关键的问题是孤子的稳定性，随着能量（范数）增加，孤子会因对称性破缺而变得不稳定，并在更高能量时恢复稳定性。基于系统的连续波（零维）对应物，通过解析近似找到了芯间耦合常数的边界值，超过该值孤子完全稳定。该近似与一维和二维孤子的数值结果显示出良好的一致性。二维孤子稳定性极限的数值结果通过计算小扰动的特征值获得，并在直接模拟中得到验证。尽管大部分孤子族是不稳定的，但不稳定性相当微弱。通过模拟研究了PT对称耦合器中二维孤子之间的碰撞。碰撞结果是非弹性的，但不会破坏PT对称性，因此不会造成破坏。
