Unstable normalized standing waves for the space periodic NLS
Unstable normalized standing waves for the space periodic NLS
复制标题
DOI：
10.2140/apde.2019.12.1177
复制
发表时间：
2017-06
期刊：
影响因子：
2.2
通讯作者：
Nils Ackermann;T. Weth
中科院分区：
文献类型：
--
作者：
Nils Ackermann;T. Weth
For the stationary nonlinear Schrodinger equation $-\Delta u+ V(x)u- f(u) = \lambda u$ with periodic potential $V$ we study the existence and stability properties of multibump solutions with prescribed $L^2$-norm. To this end we introduce a new nondegeneracy condition and develop new superposition techniques which allow to match the $L^2$-constraint. In this way we obtain the existence of infinitely many geometrically distinct solutions to the stationary problem. We then calculate the Morse index of these solutions with respect to the restriction of the underlying energy functional to the associated $L^2$-sphere, and we show their orbital instability with respect to the Schrodinger flow. Our results apply in both, the mass-subcritical and the mass-supercritical regime.
