论文标题
对数毛 - 彼得斯基方程
Logarithmic Gross-Pitaevskii equation
论文作者
论文摘要
我们考虑在无穷大处具有对数非线性和非平凡边界条件的schr {Ö} dinger方程。我们证明，在能量空间中，凯奇的问题在全球范围内很好地构成，事实证明，该问题与标准的Gross-Pitaevskii方程的能量空间相对应。然后，我们在一维情况下表征孤立的波浪和行进波。
We consider the Schr{ö}dinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, which turns out to correspond to the energy space for the standard Gross-Pitaevskii equation with a cubic nonlinearity, in small dimensions. We then characterize the solitary and travelling waves in the one dimensional case.
