On stability and instability of standing waves for the inhomogeneous fractional Schrodinger equation
In this paper, we consider the stability and instability of standing waves for the inhomogeneous fractional Schrödinger equation \[ i\partial_t\psi=(-\Delta)^s\psi- |x|^{-b}|\psi|^{2p}\psi. \] By applying the profile decomposition of bounded sequences in $H^s$ and variational methods, in the $L^...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020405/fulltext.html |
| Summary: | In this paper, we consider the stability and instability of standing waves for the inhomogeneous fractional Schrödinger equation \[ i\partial_t\psi=(-\Delta)^s\psi- |x|^{-b}|\psi|^{2p}\psi. \] By applying the profile decomposition of bounded sequences in $H^s$ and variational methods, in the $L^2$-subcritical case, i.e., $0 < p < \frac{4s-2b}{N}$, we prove that the standing waves are orbitally stable. In the $L^2$-critical case, i.e., $p=\frac{4s-2b}{N}$, we show that the standing waves are strongly unstable by blow-up. |
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| ISSN: | 2473-6988 |