Instability of standing waves to the inhomogeneous nonlinear Schrödinger equation with harmonic potential
Jianqing Chen and Yue Liu
Source: Illinois J. Math. Volume 52, Number 4
(2008), 1259-1276.
Abstract
We study the instability of standing-wave solutions eiωtφω(x) to the inhomogeneous nonlinear Schrödinger equation
iϕt=−△ϕ+|x|2ϕ−|x|b|ϕ|p−1ϕ, x∈ℝN,
where b>0 and φω is a ground-state solution. The results of the instability of standing-wave solutions reveal a balance between the frequency ω of wave and the power of nonlinearity p for any fixed b>0.
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