Stability theory of solitary waves in the presence of symmetry, I

Manoussos Grillakis, Jalal Shatah, Walter Strauss

Research output: Contribution to journalArticle

Abstract

Consider an abstract Hamiltonian system which is invariant under a one-parameter unitary group of operators. By a "solitary wave" we mean a solution the time development of which is given exactly by the one-parameter group. We find sharp conditions for the stability and instability of solitary waves. Applications are given to bound states and traveling waves of nonlinear PDEs such Klein-Gordon and Schrödinger equations.

Original languageEnglish (US)
Pages (from-to)160-197
Number of pages38
JournalJournal of Functional Analysis
Volume74
Issue number1
DOIs
StatePublished - 1987

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Stability Theory
Solitary Waves
Symmetry
Nonlinear PDE
Unitary group
Bound States
Traveling Wave
Hamiltonian Systems
Invariant
Operator

ASJC Scopus subject areas

  • Analysis

Cite this

Stability theory of solitary waves in the presence of symmetry, I. / Grillakis, Manoussos; Shatah, Jalal; Strauss, Walter.

In: Journal of Functional Analysis, Vol. 74, No. 1, 1987, p. 160-197.

Research output: Contribution to journalArticle

Grillakis, Manoussos ; Shatah, Jalal ; Strauss, Walter. / Stability theory of solitary waves in the presence of symmetry, I. In: Journal of Functional Analysis. 1987 ; Vol. 74, No. 1. pp. 160-197.
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