A. Comech and D. Pelinovsky
Purely nonlinear instability of standing waves
with minimal energy
Comm. Pure Appl. Math. 56, 1565-1607 (2003)
We consider Hamiltonian systems with U(1) symmetry.
We prove that in the generic situation
the standing wave e-i ω t φω
that has the minimal energy
among all other standing waves is unstable,
in spite of absence of linear instability.
Essentially, the instability is caused by
higher algebraic degeneracy of the zero eigenvalue
in the spectrum of the linearized system.
We apply our theory to nonlinear Schrodinger equation.
NONLINEAR SCHRODINGER EQUATION, HAMILTONIAN SYSTEMS, INSTABILITY OF NONLINEAR
WAVES, MULTIPLE EIGENVALUES, NORMAL FORMS