Scattering for the Gross-Pitaevskii equation
Scattering for the Gross-Pitaevskii equation
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DOI：
10.4310/mrl.2006.v13.n2.a8
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发表时间：
2005-10
期刊：
影响因子：
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通讯作者：
S. Gustafson;K. Nakanishi;Tai-Peng Tsai
中科院分区：
文献类型：
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作者：
S. Gustafson;K. Nakanishi;Tai-Peng Tsai
本文研究了Gross-Pitaevskii（或Ginzburg-Landau Schroedinger）方程在时间无穷远时非零常数平衡点附近解的渐近行为。我们证明了，在尺寸大于3，小扰动可以近似在时间无穷远的线性化的发展，和波算子在一定的Sobolev空间是同胚的。
We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau Schroedinger) equation. We prove that, in dimensions larger than 3, small perturbations can be approximated at time infinity by the linearized evolution, and the wave operators are homeomorphic around 0 in certain Sobolev spaces.