D.E. Pelinovsky and R.H.J. Grimshaw
Asymptotic methods in soliton stability theory
Advances in Fluid Mechanics Series, 12:
Nonlinear Instability Analysis, edited by L.Debnath and S.R.Choudhury,
(Computational Mechanics Publications, Southampton, Boston, 1997),
Energy-conserving nonlinear evolution equations are studied;
for those a Lyapunov functional exists generating stationary
soliton solutions through a constrained variational principle.
In many cases the stability of soliton solutions is determined
by a potential function. For the case where the soliton solutions
are unstable a modification of bifurcation analysis is used
to study the structure of eigenvalues and unstable eigenmodes.
An asymptotic multi-scale expansion technique is proposed and
typical scenarios of instability-induced soliton dynamics
INSTABILITY BIFURCATIONS, LYAPUNOV FUNCTIONALS, ENERGY METHODS