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 -