Xu Si-Liu, Cheng Jia-Xi, Belić Milivoj R, Hu Zheng-Long, Zhao Yuan
Opt Express. 2016 May 2;24(9):10066-77. doi: 10.1364/OE.24.010066.
We derive analytical solutions to the cubic-quintic nonlinear Schrödinger equation with potentials and nonlinearities depending on both propagation distance and transverse space. Among other, circle solitons and multi-peaked vortex solitons are found. These solitary waves propagate self-similarly and are characterized by three parameters, the modal numbers m and n, and the modulation depth of intensity. We find that the stable fundamental solitons with m = 0 and the low-order solitons with m = 1, n ≤ 2 can be supported with the energy eigenvalues E = 0 and E ≠ 0. However, higher-order solitons display unstable propagation over prolonged distances. The stability of solutions is examined by numerical simulations.
我们推导了具有依赖于传播距离和横向空间的势和非线性的三次 - 五次非线性薛定谔方程的解析解。除此之外,还发现了圆形孤子和多峰涡旋孤子。这些孤立波以自相似的方式传播,并由三个参数表征,即模式数m和n以及强度调制深度。我们发现,m = 0的稳定基态孤子和m = 1、n≤2的低阶孤子可以在能量本征值E = 0和E≠0的情况下得到支持。然而,高阶孤子在长时间传播中表现出不稳定的传播。通过数值模拟研究了解的稳定性。