论文标题
在第三维中具有周期性潜力的总木材方程的解决方案
Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Three
论文作者
论文摘要
研究了尺寸三个方程的总岩体方程的准周期溶液。事实证明，存在一个广泛的“非共振”设置$ {\ Mathcal g} \ subset \ mathbb {r}^3 $，以至于每个$ \ vec k \ in \ in \ mathcal g $ in \ nathcal g $都有一个解决方案，一个解决方案在平面波$ ae^^i \ langle {i \ langle {i \ langle { } \ rangle} $作为$ | \ vec k | \ to \ infty $，给定$ a $足够小。
Quasi-periodic solutions of the Gross-Pitaevskii equation with a periodic potential in dimension three are studied. It is proven that there is an extensive "non-resonant" set ${\mathcal G} \subset \mathbb{R}^3$ such that for every $\vec k\in \mathcal G$ there is a solution asymptotically close to a plane wave $Ae^{i\langle{ \vec{k}, \vec{x} }\rangle}$ as $|\vec k|\to \infty $, given $A$ is sufficiently small.
