Stability of bound states of Hamiltonian PDEs in the degenerate cases

Masaya Maeda

doi:10.1016/j.jfa.2012.04.006

Stability of bound states of Hamiltonian PDEs in the degenerate cases

Masaya Maeda

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

Abstract

We consider a Hamiltonian systems which is invariant under a one-parameter unitary group and give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear Klein-Gordon equation and the double power nonlinear Schrödinger equation.

Original language	English
Pages (from-to)	511-528
Number of pages	18
Journal	Journal of Functional Analysis
Volume	263
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2012.04.006
Publication status	Published - 2012 Jul 15

Keywords

Bound states
Nonlinear Klein-Gordon equation
Nonlinear Schrödinger equation
Orbital stability

ASJC Scopus subject areas

Analysis

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title = "Stability of bound states of Hamiltonian PDEs in the degenerate cases",

abstract = "We consider a Hamiltonian systems which is invariant under a one-parameter unitary group and give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear Klein-Gordon equation and the double power nonlinear Schr{\"o}dinger equation.",

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PY - 2012/7/15

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N2 - We consider a Hamiltonian systems which is invariant under a one-parameter unitary group and give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear Klein-Gordon equation and the double power nonlinear Schrödinger equation.

AB - We consider a Hamiltonian systems which is invariant under a one-parameter unitary group and give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear Klein-Gordon equation and the double power nonlinear Schrödinger equation.

KW - Bound states

KW - Nonlinear Klein-Gordon equation

KW - Nonlinear Schrödinger equation

KW - Orbital stability

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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