Stability theory of solitary waves in the presence of symmetry. II. (English) Zbl 0711.58013

Grillakis, Manoussos G.; Shatah, Jalal; Strauss, Walter

J. Funct. Anal. 94, No. 2, 308-348 (1990).

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

Keywords:

traveling waves; instability; Hamiltonian system; group invariance; solitary waves; bound states

Citations:

Zbl 0656.35122

References:

[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
[2]	Blanchard, P.; Stubbe, J.; Vazquez, L., Ann. Inst. H. Poincaré, 47, 309-336 (1987) · Zbl 0649.35076
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[8]	Strauss, W., Stability theory of solitary waves with invariants, Abstracts Amer. Math. Soc., 7, 72 (Jan. 1986)