The full text of this article is unavailable through your IP address: 3.133.124.80
Contents Online
Dynamics of Partial Differential Equations
Volume 20 (2023)
Number 4
Threshold solutions for the 3D focusing cubic-quintic nonlinear Schrödinger equation at low frequencies
Pages: 263 – 297
DOI: https://dx.doi.org/10.4310/DPDE.2023.v20.n4.a1
Authors
Abstract
This paper addresses the focusing cubic-quintic nonlinear Schrödinger equation in three space dimensions. Especially, we study the global dynamics of solutions whose energy and mass equal to those of the ground state in the spirits of Duyckaerts and Merle $\href{ https://doi.org/10.1007/s00039-009-0707-x}{[14]}$. When we try to obtain the corresponding results of [14], we meet several difficulties due to the cubic-quintic nonlinearity. We overcome them by using the one-pass theorem (no return theorem) developed by Nakanishi and Schlag $\href{ https://doi.org/10.1007/s00526-011-0424-9}{[38]}$.
Keywords
nonlinear Schrödinger equations, threshold solutions, global dynamics, ground state, blowup, scattering, special solutions, conservation laws, virial identity, one-pass theorem
2010 Mathematics Subject Classification
Primary 35B40, 35Q55. Secondary 35B44, 35P25.
The authors would like to thank the anonymous referee for his/her careful reading. M. H. was supported by JSPS KEKENHI Grant Number JP22J00787. H.K. was supported by JSPS KAKENHI Grant Number JP20K03706. M.W was supported by JSPS KAKENHI Grant Number JP22J10027.
Received 25 March 2023
Published 1 November 2023