Stability theory of solitary waves in the presence of symmetry. I.(English)Zbl 0656.35122
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.
MSC:
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 35G20 | Nonlinear higher-order PDEs |
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
Keywords:
Hamiltonian system;one-parameter unitary group;solitary wave;stability;instability;bound states;traveling waves;Klein-Gordon;SchrödingerCite
Full Text:DOI
References:
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