On minimal non-scattering solution for focusing mass-subcritical nonlinear Schr\"odinger equation

Satoshi Masaki

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arXiv · 1301.1742

On minimal non-scattering solution for focusing mass-subcritical nonlinear Schr\"odinger equation

Satoshi Masaki

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Abstract

We consider time global behavior of solutions to the focusing mass-subcritical NLS equation in weighted $L^2$ space. We prove that there exists a threshold solution such that (i) it does not scatter; (ii) with respect to a certain scale-invariant quantity, this solution attains minimum value in all non-scattering solutions. In the mass-critical case, it is known that ground states are this kind of threshold solution. However, in our case, it turns out that the above threshold solution is not a standing-wave solution.

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Satoshi Masaki. 2013-01-09. On minimal non-scattering solution for focusing mass-subcritical nonlinear Schr\"odinger equation. https://arxiv.org/abs/1301.1742

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