On uniqueness of multi-bubble blow-up solutions and multi-solitons to L^2-critical NLS

2023.9.12 15:00 S613

We are concerned with the focusing L^2-critical nonlinear Schrodinger equations. The uniqueness is proved for a large energy class of multi-bubble blow-up solutions, which converge to a sum of K pseudo-conformal blow-up solutions particularly with the low rate (T-t)^{0+}. Moreover, we also prove the uniqueness in the energy class of multi-solitons which converge to a sum of K solitary waves with convergence rate (1/t)^{2+}. The uniqueness class is further enlarged to contain the multi-solitons with even lower convergence rate (1/t)^{1/2+} in the pseudo-conformal space. This talk is based on a joint work with Prof. Cao Daomin and Prof. Zhang Deng.