Recent results on threshold solutions for the double power nonlinear Schrödinger equations (Nonlinear and Random Waves)

Abstract

In this note, we report our recent results in [23], which are concerned with 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 a spirit of Duycaerts and Merle [13]. When we try to obtain the corresponding results of [13], 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 [35].