The nonlinear Schrödinger equation ground states on product spaces
The nonlinear Schrödinger equation ground states on product spaces
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产品空间上的非线性薛定谔方程基态
DOI：
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发表时间：
2012
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通讯作者：
N. Visciglia
中科院分区：
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作者：
S. Terracini;N. Tzvetkov;N. Visciglia
研究了乘积空间$R^n上非线性Schr“odinger方程基态的性质 imes M^k$，其中$M^k$是紧黎曼流形。我们证明，对于较小的$L^2$质量，基态与相应的$R^n$基态重合。我们还证明了，在临界质量以上的基态有非平凡的$M^k$的依赖。最后，我们解决了Cauchy问题的问题，将变分分析转化为动力学稳定性结果。
We study the nature of the Nonlinear Schr"odinger equation ground states on the product spaces $R^n imes M^k$, where $M^k$ is a compact Riemannian manifold. We prove that for small $L^2$ masses the ground states coincide with the corresponding $R^n$ ground states. We also prove that above a critical mass the ground states have nontrivial $M^k$ dependence. Finally, we address the Cauchy problem issue which transform the variational analysis to dynamical stability results.