On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation

Abstract

We study the asymptotic behavior of large data radial solutions to the focusing Schrödinger equation iut +∆u = -|u| 2 u in R 3 , assuming globally bounded H 1 (R 3 ) norm (i.e.no blowup in the energy space).We show that as t → ±∞, these solutions split into the sum of three terms: a radiation term that evolves according to the linear Schrödinger equation, a smooth function localized near the origin, and an error that goes to zero in the Ḣ1 (R 3 ) norm.Furthermore, the smooth function near the origin is either zero (in which case one has scattering to a free solution), or has mass and energy bounded strictly away from zero, and obeys an asymptotic Pohozaev identity.These results are consistent with the conjecture of soliton resolution.

Locations

• Dynamics of Partial Differential Equations - View - PDF
• arXiv (Cornell University) - View - PDF
• arXiv (Cornell University) - PDF
• Dynamics of Partial Differential Equations - View - PDF
• arXiv (Cornell University) - View - PDF
• arXiv (Cornell University) - PDF