论文标题
最小化$ \ mathbb {r} \ times \ mathbb {t} $的GROSS-PITAEVSKII方程的行进波
Minimizing travelling waves for the Gross-Pitaevskii equation on $\mathbb{R} \times \mathbb{T}$
论文作者
论文摘要
我们在两个方向上周期性条件$ \ Mathbb {r} \ times \ Mathbb {t} _l $ where $ l> 0 $> 0 $ and $ l> 0 $ and $ \ mathbb {t} _l _l = \ mathiiation contery coption-pocoti包括在固定动量约束下最小化金茨堡 - 兰道能量。我们证明，$ l $以下的阈值是一个维度的阈值，这是一维的深色孤子，而不是最小化可以是一维的。
We study the Gross-Pitaevskii equation in dimension two with periodic conditions in one direction, or equivalently on the product space $\mathbb{R} \times \mathbb{T}_L$ where $L > 0$ and $\mathbb{T}_L = \mathbb{R} / L \mathbb{Z}.$ We focus on the variational problem consisting in minimizing the Ginzburg-Landau energy under a fixed momentum constraint. We prove that there exists a threshold value for $L$ below which minimizers are the one-dimensional dark solitons, and above which no minimizer can be one-dimensional.
