Threshold solutions for the focusing $L^{2}$ -supercritical NLS Equations

Qing Guo

Threshold solutions for the focusing $L^{2}$ -supercritical NLS Equations

Analysis of PDEs 2011-11-28 v1

Authors: Qing Guo

Abstract

We investigate the $L^2$ -supercritical and $\dot{H}^1$ -subcritical nonlinear Schr\"{o}dinger equation in $H^1$ . In \cite{G1} and \cite{yuan}, the mass-energy quantity $M(Q)^{\frac{1-s_{c}}{s_{c}}}E(Q)$ has been shown to be a threshold for the dynamical behavior of solutions of the equation. In the present paper, we study the dynamics at the critical level $M(u)^{\frac{1-s_{c}}{s_{c}}}E(u)=M(Q)^{\frac{1-s_{c}}{s_{c}}}E(Q)$ and classify the corresponding solutions using modulation theory, non-trivially generalize the results obtained in \cite{holmer3} for the 3D cubic Schr\"{o}dinger equation.

Keywords

nonlinear schrödinger equation nonlinear schrödinger equations

Cite

@article{arxiv.1111.5669,
  title  = {Threshold solutions for the focusing $L^{2}$ -supercritical NLS Equations},
  author = {Qing Guo},
  journal= {arXiv preprint arXiv:1111.5669},
  year   = {2011}
}

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