AI 中文总结
研究分数阶参数驱动阻尼非线性薛定谔方程中光学孤子，通过该方程框架研究孤子存在性、稳定性等，其可在激光腔实现，产生驻波和移动孤子，结果扩展了分数阶衍射介质中非线性模式种类。
AI 中文摘要
我们系统地研究了具有里兹分数阶衍射算子、立方自聚焦和线性损耗，并由线性参数驱动平衡的一维非线性薛定谔方程框架下光学孤子的存在性、稳定性和动力学。该模型可在激光腔中实现，产生驻波孤子和移动孤子，后者存在于临界速度以下。其中一种孤子在广泛参数范围内稳定，其他不稳定。分数阶衍射显著改变孤子的存在条件和稳定性阈值，还考虑了移动孤子间的碰撞。结果扩展了分数阶衍射介质中非线性模式的种类。
英文摘要
We systematically investigate the existence, stability, and dynamics of optical solitons in the framework of the one-dimensional nonlinear Schrödinger equation with the Riesz-fractional diffraction operator, cubic self-focusing, and linear loss, balanced by a linear parametric drive. The model, which can be realized in a laser cavity, produces standing and moving solitons, the latter ones existing below a critical velocity. One of the soliton species is stable in a wide range of parameters, while others are unstable. The fractional diffraction significantly alters the existence conditions and stability thresholds of the solitons. Collision between moving solitons are considered too. The results essentially expand the variety of nonlinear modes in media with fractional diffraction.
Comments11 pages, 7 figures, to be published in Phys. Rev. E
