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

Manoussos Grillakis; Jalal Shatah; Walter Strauss

doi:10.1016/0022-1236(87)90044-9

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

Manoussos Grillakis, Jalal Shatah, Walter Strauss

Mathematics

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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 language	English (US)
Pages (from-to)	160-197
Number of pages	38
Journal	Journal of Functional Analysis
Volume	74
Issue number	1
DOIs	https://doi.org/10.1016/0022-1236(87)90044-9
State	Published - Sep 1987

ASJC Scopus subject areas

Analysis

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10.1016/0022-1236(87)90044-9

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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 Schr{\"o}dinger equations.",

author = "Manoussos Grillakis and Jalal Shatah and Walter Strauss",

note = "Funding Information: * This work was supported in part by the NSF under Grants DMS 84-20957 and DMS 86-00247 and by the AR0 under Grant DAAG 29-81-K-0043. i Present address: Courant Institute, New York, NY 10012. 160",

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AU - Shatah, Jalal

AU - Strauss, Walter

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PY - 1987/9

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N2 - 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.

AB - 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.

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

Abstract

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