Threshold dynamics for the 3$d$ radial NLS with combined nonlinearity
| Autor: | Ardila, Alex H., Murphy, Jason, Zheng, Jiqiang |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider the nonlinear Schr\"odinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: \[ (i\partial_t+\Delta)u = |u|^2 u - |u|^4 u. \] In [18, 23], the authors classified the dynamics of solutions under the energy constraint $E(u)< E^c(W)$, where $W$ is the quintic NLS ground state and $E^c$ is the quintic NLS energy. In this work we classify the dynamics of $H^1$ solutions at the threshold $E(u)=E^c(W)$. Comment: 31 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|