TY - JOUR
T1 - Instability of bound states of nonlinear Schrödinger equations with Morse index equal to two
AU - Maeda, Masaya
N1 - Funding Information:
The author would like to express his deep gratitude to Reika Fukuizumi for her helpful advice and discussions. He also wishes to express his sincere appreciation to Professor Yoshio Tsutsumi for his helpful advice and encouragement. The author was supported by Grant-in-Aid for JSPS Fellows (20 ⋅ 56371) from Japan Society for the Promotion of Science. The author is grateful to the referee for reading the manuscript of this paper carefully and for offering valuable suggestions.
PY - 2010/2/1
Y1 - 2010/2/1
N2 - We prove that every bound state of the nonlinear Schrödinger equation (NLS) with Morse index equal to two, with frac(d2, d ω2) (E (φ{symbol}ω) + ω Q (φ{symbol}ω)) > 0, is orbitally unstable. We apply this result to two particular cases. One is the NLS equation with potential and the other is a system of three coupled NLS equations. In both the cases the linear instability is well known but the orbital instability results are new when the spatial dimension is high.
AB - We prove that every bound state of the nonlinear Schrödinger equation (NLS) with Morse index equal to two, with frac(d2, d ω2) (E (φ{symbol}ω) + ω Q (φ{symbol}ω)) > 0, is orbitally unstable. We apply this result to two particular cases. One is the NLS equation with potential and the other is a system of three coupled NLS equations. In both the cases the linear instability is well known but the orbital instability results are new when the spatial dimension is high.
KW - Bound states
KW - Nonlinear Schrödinger equation
KW - Orbital stability
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U2 - 10.1016/j.na.2009.10.010
DO - 10.1016/j.na.2009.10.010
M3 - Article
AN - SCOPUS:71549139746
VL - 72
SP - 2100
EP - 2113
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 3-4
ER -