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Stability theory of solitary waves in the presence of symmetry. II. (English) Zbl 0711.58013
Summary: Consider an abstract Hamiltonian system which is invariant under a group of operators. We continue to study the effect of the group invariance on the stability of solitary waves [see part I, the authors, ibid. 74, 160- 197 (1987; Zbl 0656.35122)]. Applications are given to bound states and traveling wave solutions of nonlinear wave equations.

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
35Q55 NLS equations (nonlinear Schrödinger equations)
37C75 Stability theory for smooth dynamical systems
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[1] Grillakis, M; Shatah, J; Strauss, W, Stability theory of solitary waves in the presence of symmetry, I, J. funct. anal., 74, 160-197, (1987) · Zbl 0656.35122
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