Chen Yong, Yan Zhenya, Mihalache Dumitru
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China.
Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
Phys Rev E. 2020 Jul;102(1-1):012216. doi: 10.1103/PhysRevE.102.012216.
We present an alternative type of parity-time (PT)-symmetric generalized Scarf-II potentials, which makes possible for non-Hermitian Hamiltonians in the classical linear Schrödinger system to possess fully real spectra with unique features such as the multiple PT-symmetric breaking behaviors and to support one-dimensional (1D) stable PT-symmetric solitons of power-law waveform, namely power-law solitons, in focusing Kerr-type nonlinear media. Moreover, PT-symmetric high-order solitons are also derived numerically in 1D and 2D settings. Around the exactly obtained nonlinear propagation constants, families of 1D and 2D localized nonlinear modes are also found numerically. The majority of fundamental nonlinear modes can still keep steady in general, whereas the 1D multipeak solitons and 2D vortex solitons are usually susceptible to suffering from instability. Likewise, similar results occur in the defocusing Kerr-nonlinear media. The obtained results will be useful for understanding the complex dynamics of nonlinear waves that form in PT-symmetric nonlinear media in other physical contexts.
我们提出了一种另类的宇称时间（PT）对称广义斯卡夫-II势，这使得经典线性薛定谔系统中的非厄米哈密顿量能够拥有全实谱，并具有诸如多重PT对称破缺行为等独特特征，且能在聚焦克尔型非线性介质中支持幂律波形的一维（1D）稳定PT对称孤子，即幂律孤子。此外，还在一维和二维设置中通过数值方法推导了PT对称高阶孤子。围绕精确得到的非线性传播常数，还通过数值方法找到了一维和二维局域非线性模式族。大多数基本非线性模式通常仍能保持稳定，而一维多峰孤子和二维涡旋孤子通常容易受到不稳定性的影响。同样，在散焦克尔非线性介质中也会出现类似结果。所获得的结果将有助于理解在其他物理环境中PT对称非线性介质中形成的非线性波的复杂动力学。
