On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient

Jianqing Chen

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 3, page 715-736
  • ISSN: 0011-4642

Abstract

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By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrödinger equation with harmonic potential i ϕ t = - ▵ ϕ + | x | 2 ϕ - | x | b | ϕ | p - 2 ϕ . We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave.

How to cite

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Chen, Jianqing. "On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient." Czechoslovak Mathematical Journal 60.3 (2010): 715-736. <http://eudml.org/doc/38038>.

@article{Chen2010,
abstract = {By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrödinger equation with harmonic potential \[ \{\rm i\}\varphi \_t=-\triangle \varphi +|x|^2\varphi -|x|^b|\varphi |^\{p-2\}\varphi . \] We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave.},
author = {Chen, Jianqing},
journal = {Czechoslovak Mathematical Journal},
keywords = {interpolation inequality; inhomogeneous nonlinear Schrödinger equation; harmonic potential; blow-up; global existence; standing waves; strong instability; interpolation inequality; inhomogeneous nonlinear Schrödinger equation; harmonic potential; blow-up; global existence; standing wave; strong instability},
language = {eng},
number = {3},
pages = {715-736},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient},
url = {http://eudml.org/doc/38038},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Chen, Jianqing
TI - On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 715
EP - 736
AB - By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrödinger equation with harmonic potential \[ {\rm i}\varphi _t=-\triangle \varphi +|x|^2\varphi -|x|^b|\varphi |^{p-2}\varphi . \] We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave.
LA - eng
KW - interpolation inequality; inhomogeneous nonlinear Schrödinger equation; harmonic potential; blow-up; global existence; standing waves; strong instability; interpolation inequality; inhomogeneous nonlinear Schrödinger equation; harmonic potential; blow-up; global existence; standing wave; strong instability
UR - http://eudml.org/doc/38038
ER -

References

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