PT对称非线性薛定谔方程的高维孤子生成、稳定性与激发
Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations
AI总结：
本文研究PT对称广义Scarf-II势中的一维及多维精确孤子，分析能谱、稳定性与绝热操控，并提出新型n维势以支持高维孤子实验设计。
摘要：
我们研究了一类具有物理吸引力的PT对称广义Scarf-II（GS-II）势，这类势能够在一维和多维非线性薛定谔方程中支持精确孤子。在一维和多维情形下，我们发现适当调节局域化参数可以支持完全实数的能谱。此外，还产生了基态孤子和高阶孤子的连续族。结果表明，基态是稳定的，而包括一维多峰孤子、二维孤子和三维光弹在内的高阶孤子则不稳定。进一步地，我们发现稳定孤子始终能够以鲁棒形式传播，并持续束缚在缓慢移动的GS-II型势阱中，这为操控光学孤子开辟了道路。孤子也可以通过绝热变化势参数而转化为稳定形式。最后，我们还报道了另一类n维PT对称GS-II势。这些结果将有助于进一步探索高维PT对称孤子并设计相关物理实验。
英文摘要：
We study a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials, which can support exact solitons in one- and multi-dimensional nonlinear Schrödinger equation. In the 1D and multi-D settings, we find that a properly adjusted localization parameter may support fully real energy spectra. Also, continuous families of fundamental and higher-order solitons are produced. The fundamental states are shown to be stable, while the higher-order ones, including 1D multimodal solitons, 2D solitons, and 3D light bullets, are unstable. Further, we find that the stable solitons can always propagate, in a robust form, remaining trapped in slowly moving potential wells of the GS-II type, which opens the way for manipulations of optical solitons. Solitons may also be transformed into stable forms by means of adibatic variation of potential parameters. Finally, an alternative type of n-dimensional PT-symmetric GS-II potentials is reported too. These results will be useful to further explore the higher-dimensional PT-symmetric solitons and to design the relative physical experiments.
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