Asymptotic methods in soliton stability theory

We describe asymptotic methods for the analysis of soliton stability and related long-term dynamics in nonlinear evolution equations which conserve energy. For these equations there exists a Lyapunov functional which generates stationary soliton solutions through a constrained variational principle. We show that the stability of soliton solutions is determined in many cases by a potential function given by this functional at the stationary …