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

Manoussos Grillakis, Jalal Shatah, Walter Strauss

Research output: Contribution to journalArticle


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
Issue number1
StatePublished - Sep 1987


ASJC Scopus subject areas

  • Analysis

Cite this