Threshold solutions for the 3D focusing cubic-quintic nonlinear Schrodinger equation at low frequencies

TL;DR

This paper investigates the global behavior of solutions to the 3D focusing cubic-quintic nonlinear Schrödinger equation at low frequencies, utilizing the one-pass theorem to address challenges posed by the nonlinearity.

Contribution

It extends the analysis of threshold solutions for the cubic-quintic NLS in 3D, applying the one-pass theorem to overcome nonlinearity-related difficulties.

Findings

Characterization of threshold solutions at low frequencies

Application of the one-pass theorem to cubic-quintic NLS

Insights into global dynamics near the ground state

Abstract

This paper addresses the focusing cubic-quintic nonlinear Schrodinger 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 sprits of Duyckaerts and Merle (2009). When we try to obtain the corresponding result, 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 (2012).