发表机构
University of North Carolina, Chapel Hill（北卡罗来纳大学教堂山分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究周期色散管理非线性薛定谔方程能量最大化子的正则性，证明其傅里叶系数指数衰减并解析，且解非平凡，数值实验支持结论。
AI 中文摘要
我们探讨了在长度为$L$、平均色散为零的环面上，周期色散管理光纤中固定强度下拉格朗日量能量最大化子的正则性。我们证明傅里叶系数以多项式速率衰减，然后将其提升为指数衰减，从而使得对于足够大的$L$，最大化子在空间上是解析的。此外，通过与实直线上的优化子进行渐近比较，我们证明了这些解是非平凡的。我们还考虑了一个猜想，即最大化子必然具有能量泛函和由此产生的欧拉-拉格朗日方程所固有的对称性。我们的所有结果都得到了说明性数值实验的支持。
英文摘要
We explore the regularity of energy maximizers for the Lagrangian of a periodic dispersion managed fiber optic at fixed intensity, on a torus of length $L$ and with vanishing average dispersion. We show that the Fourier coefficients decay at a polynomial rate, and then upgrade this to exponential decay, so that the maximizers are analytic in space for large enough $L$. In addition, by an asymptotic comparison to the optimizers on the real line, we prove that the solutions are non-trivial. We also consider a conjecture that the maximizer necessarily has an underlying symmetry inherent to both the energy functional and the resulting Euler-Lagrange equation. All of our results are supported with illustrative numerical experiments.
Comments27 pages, 5 figures
